Objective:To explore the application of the Registered Nurses'Association of Ontario(RNAO)Best Practice Guideline(BPG)for Developing and Sustaining Nursing Leadership through the lens of nursing students transitio...Objective:To explore the application of the Registered Nurses'Association of Ontario(RNAO)Best Practice Guideline(BPG)for Developing and Sustaining Nursing Leadership through the lens of nursing students transitioning from classroom learning to clinical practice.Through this reflection,the authors hope to inspire and empower future nursing leaders to champion innovation,resilience,and excellence in healthcare.Methods:By integrating evidence-based leadership principles,the authors reflect on their personal experiences,challenges,and successes in implementing these guidelines in real-world settings.Results:The paper highlights the significance of leadership in fostering healthy work environments and improving patient outcomes,emphasizing the role of nursing students as emerging leaders.Practical strategies for applying BPG,the RNAO BPG suggests leadership skills on professional development,and recommendations for embedding leadership principles into nursing education and practice are discussed.Conclusions:Implementing nursing leadership from the beginning of a nursing student's journey is vital for shaping the next generation of healthcare leaders.By integrating leadership principles early in nursing education,students can develop the skills needed to navigate clinical challenges,collaborate effectively with healthcare teams,and advocate for positive change.Starting with leadership guidelines in nursing school ensures that future nurses are equipped to foster supportive work environments,improve patient outcomes,and drive innovation from the very start of their careers,making leadership an inherent part of their professional identity.展开更多
Objectives This study aimed to compare the effectiveness of the semi-virtual simulation and traditional simulation teaching models based on the Standards of Best Practice(SOBP)according to the International Nursing As...Objectives This study aimed to compare the effectiveness of the semi-virtual simulation and traditional simulation teaching models based on the Standards of Best Practice(SOBP)according to the International Nursing Association for Clinical Simulation and Learning(INACSL)in the Adult Nursing course.Methods This study used a quasi-experimental design.A total of 94 third-year nursing students from a university in Beijing between November and December 2022 were recruited as participants.An innovative semi-virtual simulation teaching model was designed based on the SOBP established by the INACSL.In the Adult Nursing course,both the semi-virtual and traditional simulation teaching models were implemented.At the end of the simulation sessions,participants completed the Chinese version of the Simulation Effectiveness Tool-Modified(SET-M)to assess the effectiveness of the two teaching models.Results All nursing students completed the simulation sessions.There was no difference(t=−0.93,P=0.353)in the total scores between the semi-virtual simulation teaching model(50.87±5.30)and the traditional simulation teaching model(50.37±5.16).However,there was a statistically significant difference(t=−2.65,P=0.010)in the prebriefing section(semi-virtual simulation:5.60±0.71;traditional simulation:5.33±0.78).In contrast,no statistically significant differences were found for the scenario and debriefing sections(P>0.05).At the individual item level,statistical differences(P<0.05)between the two models were identified for items 1 and 9,but not for the remaining items(P>0.05).By analyzing the open-ended question,it was found that both simulation models were effective,and students’comments were similar.Conclusions The study demonstrated equivalent effectiveness between the semi-virtual and traditional simulation teaching models.Semi-virtual simulation teaching model could offer a more flexible and feasible approach to simulation teaching.展开更多
The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from ...The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.展开更多
The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability ...The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.展开更多
In an abstract set up, we get strong type inequalities in L^p＋1 by assuming weak or extra-weak inequalities in Orlicz spaces. For some classes of functions, the number p is related to Simonenko indices. We apply the ...In an abstract set up, we get strong type inequalities in L^p＋1 by assuming weak or extra-weak inequalities in Orlicz spaces. For some classes of functions, the number p is related to Simonenko indices. We apply the results to get strong inequal- ities for maximal functions associated to best Ф-approximation operators in an Orlicz space L^Ф.展开更多
Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.
Let L^2（[0, 1], x） be the space of the real valued, measurable, square summable functions on [0, 1] with weight x, and let n be the subspace of L2（[0, 1], x） defined by a linear combination of Jo（μkX）, where J...Let L^2（[0, 1], x） be the space of the real valued, measurable, square summable functions on [0, 1] with weight x, and let n be the subspace of L2（[0, 1], x） defined by a linear combination of Jo（μkX）, where Jo is the Bessel function of order 0 and {μk} is the strictly increasing sequence of all positive zeros of Jo. For f ∈ L^2（[0, 1], x）, let E（f, n） be the error of the best L2（[0, 1], x）, i.e., approximation of f by elements of n. The shift operator off at point x ∈[0, 1] with step t ∈[0, 1] is defined by T（t）f（x）=1/π∫0^π f（√x^2 ＋t^2-2xtcosO）dθ The differences （I- T（t））^r/2f = ∑j=0^∞（-1）^j（j^r/2）T^j（t）f of order r ∈ （0, ∞） and the L^2（[0, 1],x）- modulus of continuity ωr（f,τ） = sup{｜｜（I- T（t））^r/2f｜｜：0≤ t ≤τ] of order r are defined in the standard way, where T^0（t） = I is the identity operator. In this paper, we establish the sharp Jackson inequality between E（f, n） and ωr（f, τ） for some cases of r and τ. More precisely, we will find the smallest constant n（τ, r） which depends only on n, r, and % such that the inequality E（f, n）≤ n（τ, r）ωr（f, τ） is valid.展开更多
Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.
We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M a...We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M and the quotient space W/M.展开更多
In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables.Our approach extends and unifies several proble...In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables.Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.展开更多
In this note we obtain generalization of well known results of carbone and Conti,Sehgal and Singh and Tanimoto concerning the existence of best approximation and simultaneous best approximation of continuous Junctions...In this note we obtain generalization of well known results of carbone and Conti,Sehgal and Singh and Tanimoto concerning the existence of best approximation and simultaneous best approximation of continuous Junctions from the set up of a normed space to the case of a Hausdorff locally convex space.展开更多
In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions dependin...In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions depending on ε, when ε→ 0. It is introduced a general concept of Pade approximant and we study its relation with the best local quasi-rational approximant. We characterize the limit of the error for polynomial approximation. We also obtain a new condition over a weight function in order to obtain inequalities in Lp norm, which play an important role in problems of weighted best local Lp approximation in several variables.展开更多
Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best...Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X.We also give simultaneous characterization of elements of best approximation and also consider elements of ε-approximation.展开更多
Some new coincidence theorem s involving a new class of set_valued mappings containing composites of acyclic mappings defined in a contractible space are proved. For applications, some best approximation theorems an...Some new coincidence theorem s involving a new class of set_valued mappings containing composites of acyclic mappings defined in a contractible space are proved. For applications, some best approximation theorems and coincidence theorems for set-valued mappings are als o given. A number of known results in recent literature are improved and general ized by the theorems in this paper.展开更多
For a subset K of a metric space(X,d)and x∈X,Px(x)={y∈K:d(x,y)=d(x,K)≡inf{d(x,k):k∈K}}is called the set of best K-approximant to x.An element go E K is said to be a best simulta-neous approximation of the pair y1,...For a subset K of a metric space(X,d)and x∈X,Px(x)={y∈K:d(x,y)=d(x,K)≡inf{d(x,k):k∈K}}is called the set of best K-approximant to x.An element go E K is said to be a best simulta-neous approximation of the pair y1,y2 E∈if max{d(y1,go),d(y2,go)}=inf g∈K max{d(y1,g),d(y2,g)}.In this paper,some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved.For self mappings T and S on K,results are proved on both T-and S-invariant points for a set of best simultaneous approximation.Some results on best K-approximant are also deduced.The results proved generalize and extend some results of I.Beg and M.Abbas^[1],S.Chandok and T.D.Narang^[2],T.D.Narang and S.Chandok^[11],S.A.Sahab,M.S.Khan and S.Sessa^[14],P.Vijayaraju^[20]and P.Vijayaraju and M.Marudai^[21].展开更多
In this paper, a new concept of weakly ,convex graph for set-valued mappings is introduced and studied. By using the concept , some new coincidence, the bestapproximation and fixed point-theorems are obta...In this paper, a new concept of weakly ,convex graph for set-valued mappings is introduced and studied. By using the concept , some new coincidence, the bestapproximation and fixed point-theorems are obtained.展开更多
We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map stud...We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map studied. Our work generalizes severl results in approximation theory.展开更多
We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any ele...We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X展开更多
In this paper we investigate several solution algorithms for the convex fea- sibility problem(CFP)and the best approximation problem(BAP)respectively.The algorithms analyzed are already known before,but by adequately ...In this paper we investigate several solution algorithms for the convex fea- sibility problem(CFP)and the best approximation problem(BAP)respectively.The algorithms analyzed are already known before,but by adequately reformulating the CFP or the BAP we naturally deduce the general projection method for the CFP from well-known steepest decent method for unconstrained optimization and we also give a natural strategy of updating weight parameters.In the linear case we show the connec- tion of the two projection algorithms for the CFP and the BAP respectively.In addition, we establish the convergence of a method for the BAP under milder assumptions in the linear case.We also show by examples a Bauschke's conjecture is only partially correct.展开更多
文摘Objective:To explore the application of the Registered Nurses'Association of Ontario(RNAO)Best Practice Guideline(BPG)for Developing and Sustaining Nursing Leadership through the lens of nursing students transitioning from classroom learning to clinical practice.Through this reflection,the authors hope to inspire and empower future nursing leaders to champion innovation,resilience,and excellence in healthcare.Methods:By integrating evidence-based leadership principles,the authors reflect on their personal experiences,challenges,and successes in implementing these guidelines in real-world settings.Results:The paper highlights the significance of leadership in fostering healthy work environments and improving patient outcomes,emphasizing the role of nursing students as emerging leaders.Practical strategies for applying BPG,the RNAO BPG suggests leadership skills on professional development,and recommendations for embedding leadership principles into nursing education and practice are discussed.Conclusions:Implementing nursing leadership from the beginning of a nursing student's journey is vital for shaping the next generation of healthcare leaders.By integrating leadership principles early in nursing education,students can develop the skills needed to navigate clinical challenges,collaborate effectively with healthcare teams,and advocate for positive change.Starting with leadership guidelines in nursing school ensures that future nurses are equipped to foster supportive work environments,improve patient outcomes,and drive innovation from the very start of their careers,making leadership an inherent part of their professional identity.
文摘Objectives This study aimed to compare the effectiveness of the semi-virtual simulation and traditional simulation teaching models based on the Standards of Best Practice(SOBP)according to the International Nursing Association for Clinical Simulation and Learning(INACSL)in the Adult Nursing course.Methods This study used a quasi-experimental design.A total of 94 third-year nursing students from a university in Beijing between November and December 2022 were recruited as participants.An innovative semi-virtual simulation teaching model was designed based on the SOBP established by the INACSL.In the Adult Nursing course,both the semi-virtual and traditional simulation teaching models were implemented.At the end of the simulation sessions,participants completed the Chinese version of the Simulation Effectiveness Tool-Modified(SET-M)to assess the effectiveness of the two teaching models.Results All nursing students completed the simulation sessions.There was no difference(t=−0.93,P=0.353)in the total scores between the semi-virtual simulation teaching model(50.87±5.30)and the traditional simulation teaching model(50.37±5.16).However,there was a statistically significant difference(t=−2.65,P=0.010)in the prebriefing section(semi-virtual simulation:5.60±0.71;traditional simulation:5.33±0.78).In contrast,no statistically significant differences were found for the scenario and debriefing sections(P>0.05).At the individual item level,statistical differences(P<0.05)between the two models were identified for items 1 and 9,but not for the remaining items(P>0.05).By analyzing the open-ended question,it was found that both simulation models were effective,and students’comments were similar.Conclusions The study demonstrated equivalent effectiveness between the semi-virtual and traditional simulation teaching models.Semi-virtual simulation teaching model could offer a more flexible and feasible approach to simulation teaching.
文摘The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.
文摘The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.
基金supported by Consejo Nacional de Investigaciones Científicas y Técnicas(CONICET)and Universidad Nacional de San Luis(UNSL)with grants PIP 11220110100033CO and PROICO 317902
文摘In an abstract set up, we get strong type inequalities in L^p＋1 by assuming weak or extra-weak inequalities in Orlicz spaces. For some classes of functions, the number p is related to Simonenko indices. We apply the results to get strong inequal- ities for maximal functions associated to best Ф-approximation operators in an Orlicz space L^Ф.
文摘Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.
基金supported partly by National Natural Science Foundation of China (No.10471010)partly by the project"Representation Theory and Related Topics"of the"985 Program"of Beijing Normal University and Beijing Natural Science Foundation (1062004).
文摘Let L^2（[0, 1], x） be the space of the real valued, measurable, square summable functions on [0, 1] with weight x, and let n be the subspace of L2（[0, 1], x） defined by a linear combination of Jo（μkX）, where Jo is the Bessel function of order 0 and {μk} is the strictly increasing sequence of all positive zeros of Jo. For f ∈ L^2（[0, 1], x）, let E（f, n） be the error of the best L2（[0, 1], x）, i.e., approximation of f by elements of n. The shift operator off at point x ∈[0, 1] with step t ∈[0, 1] is defined by T（t）f（x）=1/π∫0^π f（√x^2 ＋t^2-2xtcosO）dθ The differences （I- T（t））^r/2f = ∑j=0^∞（-1）^j（j^r/2）T^j（t）f of order r ∈ （0, ∞） and the L^2（[0, 1],x）- modulus of continuity ωr（f,τ） = sup{｜｜（I- T（t））^r/2f｜｜：0≤ t ≤τ] of order r are defined in the standard way, where T^0（t） = I is the identity operator. In this paper, we establish the sharp Jackson inequality between E（f, n） and ωr（f, τ） for some cases of r and τ. More precisely, we will find the smallest constant n（τ, r） which depends only on n, r, and % such that the inequality E（f, n）≤ n（τ, r）ωr（f, τ） is valid.
文摘Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.
文摘We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M and the quotient space W/M.
基金Supported by Universidad Nacional de Rfo Cuaito and CONICET.
文摘In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables.Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.
文摘In this note we obtain generalization of well known results of carbone and Conti,Sehgal and Singh and Tanimoto concerning the existence of best approximation and simultaneous best approximation of continuous Junctions from the set up of a normed space to the case of a Hausdorff locally convex space.
基金This work is supported by Universidad Nacional de Rio Cuarto.
文摘In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions depending on ε, when ε→ 0. It is introduced a general concept of Pade approximant and we study its relation with the best local quasi-rational approximant. We characterize the limit of the error for polynomial approximation. We also obtain a new condition over a weight function in order to obtain inequalities in Lp norm, which play an important role in problems of weighted best local Lp approximation in several variables.
文摘Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X.We also give simultaneous characterization of elements of best approximation and also consider elements of ε-approximation.
文摘Some new coincidence theorem s involving a new class of set_valued mappings containing composites of acyclic mappings defined in a contractible space are proved. For applications, some best approximation theorems and coincidence theorems for set-valued mappings are als o given. A number of known results in recent literature are improved and general ized by the theorems in this paper.
文摘For a subset K of a metric space(X,d)and x∈X,Px(x)={y∈K:d(x,y)=d(x,K)≡inf{d(x,k):k∈K}}is called the set of best K-approximant to x.An element go E K is said to be a best simulta-neous approximation of the pair y1,y2 E∈if max{d(y1,go),d(y2,go)}=inf g∈K max{d(y1,g),d(y2,g)}.In this paper,some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved.For self mappings T and S on K,results are proved on both T-and S-invariant points for a set of best simultaneous approximation.Some results on best K-approximant are also deduced.The results proved generalize and extend some results of I.Beg and M.Abbas^[1],S.Chandok and T.D.Narang^[2],T.D.Narang and S.Chandok^[11],S.A.Sahab,M.S.Khan and S.Sessa^[14],P.Vijayaraju^[20]and P.Vijayaraju and M.Marudai^[21].
文摘In this paper, a new concept of weakly ,convex graph for set-valued mappings is introduced and studied. By using the concept , some new coincidence, the bestapproximation and fixed point-theorems are obtained.
文摘We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map studied. Our work generalizes severl results in approximation theory.
文摘We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X
基金supported by the National Natural Science Foundation of China,Grant 10571134
文摘In this paper we investigate several solution algorithms for the convex fea- sibility problem(CFP)and the best approximation problem(BAP)respectively.The algorithms analyzed are already known before,but by adequately reformulating the CFP or the BAP we naturally deduce the general projection method for the CFP from well-known steepest decent method for unconstrained optimization and we also give a natural strategy of updating weight parameters.In the linear case we show the connec- tion of the two projection algorithms for the CFP and the BAP respectively.In addition, we establish the convergence of a method for the BAP under milder assumptions in the linear case.We also show by examples a Bauschke's conjecture is only partially correct.
