For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Feket...For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Fekete-Szeg o functional.展开更多
In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell...In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell shaped region in the open unit disc ?.展开更多
The main objective of this paper is to derive the upper bounds for the coefficients of functions in a subclass of analytic and bi-univalent functions associated with Faber polynomials. The consequences presented here ...The main objective of this paper is to derive the upper bounds for the coefficients of functions in a subclass of analytic and bi-univalent functions associated with Faber polynomials. The consequences presented here point out and correct the errors of some earlier results.展开更多
In this paper, we investigate the bounds of the coefficients of several classes of meromorphic bi-univalent functions. The results presented in this paper improve or generalize the recent works of other authors.
In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a...In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a2| and |a3| for functions in these new subclasses. The results presented in this paper improve or generalize the recent works of other authors.展开更多
The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson'...The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.展开更多
In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions o...In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions of the class. Moreover, we verify Brannan and Clunie＇s conjecture ｜a_2｜ ≤2^（1/2）for some of our classes. The results in this paper extend many results recently researched by many authors.展开更多
In this paper, we estimate the Fekete-Szego functional with k-th root transform for the inverse of certain classes of analytic univalent functions using quasi-subordination.
In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors.
In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient c...In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient conditions,extreme points,distortion bounds and partial sums properties for the functions belonging to the subclasses are obtained.展开更多
Let A be the space of functions analytic in the unit disk D = {z：｜z｜ 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0 and｜f＇（z）（z/f（z））2-1｜〈1（｜z｜〈1...Let A be the space of functions analytic in the unit disk D = {z：｜z｜ 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0 and｜f＇（z）（z/f（z））2-1｜〈1（｜z｜〈1）.Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0and｜zf＇（z）-f（z）｜〈1/2（｜z｜〈1）.In this article,we discuss the properties of U and Ω.展开更多
In this paper, we introduce a new subclass of bi-univalent functions defined by quasi-subordination and Hohlov operator and obtain the coefficient estimates and Fekete-Szego inequality for function in this new subclas...In this paper, we introduce a new subclass of bi-univalent functions defined by quasi-subordination and Hohlov operator and obtain the coefficient estimates and Fekete-Szego inequality for function in this new subclass. The results presented in this paper improve or generalize the recent works of other authors.展开更多
By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several propertie...By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several properties and characteristics including(for example)the modified Hadamard products,Holder's inequalities and convolution properties as well as some closure properties under a general family of integral transforms.展开更多
In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Fu...In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients ｜a2｜ and ｜a3｜ for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Several （known or new） consequences of the results are also pointed out.展开更多
We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l2 space, we obt...We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l2 space, we obtain some new characterizations of quasiconformal extendablity and asymptotic conformality for univalent functions.展开更多
A new characterization of univalent Bloch functions is given by investigating the growth order of an essentially increasing function. Our contribution can be considered as a slight improvement of the well-known Pommer...A new characterization of univalent Bloch functions is given by investigating the growth order of an essentially increasing function. Our contribution can be considered as a slight improvement of the well-known Pommerenke's result and its all generalizations, and the proof presented in this paper is independently developed.展开更多
In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel function...In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z（Bκ＋1^c f（z））′= κBκ^c f（z）-（κ- 1）Bκ＋1^c f（z）,where b, c, p ∈ C and κ = p ＋（b ＋ 1）/2 ∈ C ／ Z0^-（Z0^-= {0,-1,-2, … }）. The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.展开更多
Let A be the class of functions f(z)=z+sum from n=2 to ∞ (a_nZ^n) which are analytic in the unit disc, and let In this paper, Some properties of Q_α(β) and R_α(β) are investigated. In particular, Some results due...Let A be the class of functions f(z)=z+sum from n=2 to ∞ (a_nZ^n) which are analytic in the unit disc, and let In this paper, Some properties of Q_α(β) and R_α(β) are investigated. In particular, Some results due to chichra [4], Mocanu[5] and Obradovic[6] are extended. In addition, We also showed an error of S. Owa[8].展开更多
This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z ： ｜z｜〈 1} satisfying the conditions that f（0） =0, f＇（0）= 1, and α（1＋zf＇＇（z）/f＇（...This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z ： ｜z｜〈 1} satisfying the conditions that f（0） =0, f＇（0）= 1, and α（1＋zf＇＇（z）/f＇（z）＋（1-α）zf＇（z）/f（z）∈p（U）for all z ∈ U, where αis a real number and p（z）=1＋r^2z^2/1-Tz-T^2z^2（z∈ U）. The number T = （1 -√5）/2 is such that T^2 = 1 ＋ T. The class SFLMa introduced by J. Dziok, R.K. Raina, and J. Sokot [3, Appl. Math. Comput. 218 （2011）, 996-1002] is closely related to the classes of starlike and convex functions. The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.展开更多
文摘For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Fekete-Szeg o functional.
文摘In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell shaped region in the open unit disc ?.
基金Supported by the National Natural Science Foundation of China(Grant No.11401041)
文摘The main objective of this paper is to derive the upper bounds for the coefficients of functions in a subclass of analytic and bi-univalent functions associated with Faber polynomials. The consequences presented here point out and correct the errors of some earlier results.
基金Supported by the Natural Science Foundation of Anhui Provincial Department of Education(Grant Nos.KJ2018-A0833 KJ2018A0839)
文摘In this paper, we investigate the bounds of the coefficients of several classes of meromorphic bi-univalent functions. The results presented in this paper improve or generalize the recent works of other authors.
基金The NSF(KJ2015A372) of Anhui Provincial Department of Education
文摘In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a2| and |a3| for functions in these new subclasses. The results presented in this paper improve or generalize the recent works of other authors.
文摘The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.
基金Supported by the National Natural Science Foundation of China(Grant No.11401186)the Research Fund from Engineering and Technology College Yangtze University(Grant No.15J0802)
文摘In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions of the class. Moreover, we verify Brannan and Clunie＇s conjecture ｜a_2｜ ≤2^（1/2）for some of our classes. The results in this paper extend many results recently researched by many authors.
基金Supported by the National Natural Science Foundation of China (Grant No. 11561001)the Natural Science Foundation of Inner Mongolia of China (Grant No. 2018MS01026)+4 种基金the Natural Science Foundation of Anhui Provincial Department of Education (Grant Nos. KJ2018A0833KJ2020A0993KJ2020ZD74)Provincial Quality Engineering Project of Anhui Colleges and Universities (Grant No. 2018mooc608)the Key Cultivated Project at School Level of the National Science Fund of Guangzhou Civil Aviation College (Grant No. 18X0428)。
文摘In this paper, we estimate the Fekete-Szego functional with k-th root transform for the inverse of certain classes of analytic univalent functions using quasi-subordination.
基金supported by NSFC(11071058)Educational Commission of Hubei Province of China(D2011006)
文摘In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors.
基金Supported by the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant No.2019MS01023)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant Nos.NJZZ19209,NJZY20198).
文摘In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient conditions,extreme points,distortion bounds and partial sums properties for the functions belonging to the subclasses are obtained.
基金Supported by the Key Laboratory of Applied Mathematics in Hubei Province,China
文摘Let A be the space of functions analytic in the unit disk D = {z：｜z｜ 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0 and｜f＇（z）（z/f（z））2-1｜〈1（｜z｜〈1）.Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0and｜zf＇（z）-f（z）｜〈1/2（｜z｜〈1）.In this article,we discuss the properties of U and Ω.
基金The NSF(11561001)of Chinathe NSF(2014MS0101)of Inner Mongolia Province+1 种基金the Higher School Foundation(NJZY19211)of Inner Mongolia of Chinathe NSF(KJ2018A0839,KJ2018A0833)of Anhui Provincial Department of Education
文摘In this paper, we introduce a new subclass of bi-univalent functions defined by quasi-subordination and Hohlov operator and obtain the coefficient estimates and Fekete-Szego inequality for function in this new subclass. The results presented in this paper improve or generalize the recent works of other authors.
文摘By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several properties and characteristics including(for example)the modified Hadamard products,Holder's inequalities and convolution properties as well as some closure properties under a general family of integral transforms.
文摘In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients ｜a2｜ and ｜a3｜ for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Several （known or new） consequences of the results are also pointed out.
基金supported by the Program for New Century Excellent Talents in University (Grant No. 06-0504)National Natural Science Foundation of China (Grant No. 10771153)
文摘We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l2 space, we obtain some new characterizations of quasiconformal extendablity and asymptotic conformality for univalent functions.
基金Project supported by the National Natural Science Foundation of China.
文摘We make improvements to some of the constants concerned with univalent functions with quasiconformal extensions that have appeared in the literature.
基金This research was supported in part by a grant from the Vaisala Fund, Finland
文摘A new characterization of univalent Bloch functions is given by investigating the growth order of an essentially increasing function. Our contribution can be considered as a slight improvement of the well-known Pommerenke's result and its all generalizations, and the proof presented in this paper is independently developed.
基金partly supported by the Natural Science Foundation of China(11271045)the Higher School Doctoral Foundation of China(20100003110004)+2 种基金the Natural Science Foundation of Inner Mongolia of China(2010MS0117)athe Higher School Foundation of Inner Mongolia of China(NJZY13298)the Commission for the Scientific Research Projects of Kafkas Univertsity(2012-FEF-30)
文摘In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z（Bκ＋1^c f（z））′= κBκ^c f（z）-（κ- 1）Bκ＋1^c f（z）,where b, c, p ∈ C and κ = p ＋（b ＋ 1）/2 ∈ C ／ Z0^-（Z0^-= {0,-1,-2, … }）. The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.
文摘Let A be the class of functions f(z)=z+sum from n=2 to ∞ (a_nZ^n) which are analytic in the unit disc, and let In this paper, Some properties of Q_α(β) and R_α(β) are investigated. In particular, Some results due to chichra [4], Mocanu[5] and Obradovic[6] are extended. In addition, We also showed an error of S. Owa[8].
文摘This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z ： ｜z｜〈 1} satisfying the conditions that f（0） =0, f＇（0）= 1, and α（1＋zf＇＇（z）/f＇（z）＋（1-α）zf＇（z）/f（z）∈p（U）for all z ∈ U, where αis a real number and p（z）=1＋r^2z^2/1-Tz-T^2z^2（z∈ U）. The number T = （1 -√5）/2 is such that T^2 = 1 ＋ T. The class SFLMa introduced by J. Dziok, R.K. Raina, and J. Sokot [3, Appl. Math. Comput. 218 （2011）, 996-1002] is closely related to the classes of starlike and convex functions. The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.
