This paper is an attempt to investigate systematically fixed points of weakly inward maps by using some basic results from differential equations in Banach spaces. By investigating the Poincare operators for such diff...This paper is an attempt to investigate systematically fixed points of weakly inward maps by using some basic results from differential equations in Banach spaces. By investigating the Poincare operators for such differential equations, we establish a fixed point index theory for two classes of weakly inward maps.展开更多
In this paper first we prove common fixed point theorems for compatible and weakly compatible maps. Secondly, we prove common fixed point theorems for weakly compatible maps along with property (E.A.) and (CLRg) prope...In this paper first we prove common fixed point theorems for compatible and weakly compatible maps. Secondly, we prove common fixed point theorems for weakly compatible maps along with property (E.A.) and (CLRg) property respectively.展开更多
The notion of a G-symmetric space is introduced and the common fixed points for some pairs of occasionally weakly compatible maps satisfying some contractive conditions in a G-symmetric space are proved. The results e...The notion of a G-symmetric space is introduced and the common fixed points for some pairs of occasionally weakly compatible maps satisfying some contractive conditions in a G-symmetric space are proved. The results extend and improve some results in literature.展开更多
The aim of this paper is to establish some new common fixed point theorems for generalized contractive maps in fuzzy metric space by using property (E.A.), common property (E.A.), JCLRST property and CLRS property. Ou...The aim of this paper is to establish some new common fixed point theorems for generalized contractive maps in fuzzy metric space by using property (E.A.), common property (E.A.), JCLRST property and CLRS property. Our results improve and extend the results of Chauhan et al. [1] and Sedghi et al. [2] besides several known results. We also furnish an illustrative example in support of our results.展开更多
In this paper, we mainly discuss the images of certain spaces under closed sequencecovering maps. It is showed that the property with a locally countable weak base is preserved by closed sequence-covering maps. And th...In this paper, we mainly discuss the images of certain spaces under closed sequencecovering maps. It is showed that the property with a locally countable weak base is preserved by closed sequence-covering maps. And the following question is discussed： Are the closed sequence-covering images of spaces with a point-countable sn-network sn-first countable？展开更多
Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K ...Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.展开更多
In this paper, we introduce the concepts of weakly R-KKM mappings, R- convex and R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topolo...In this paper, we introduce the concepts of weakly R-KKM mappings, R- convex and R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan＇s matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature.展开更多
The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a usef...The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a useful inequality is obtained, which can be used to derive the self-improving regularity.展开更多
In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is ...In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.展开更多
In this paper, some new existence and uniqueness of points of coincidence of weakly compatible pair of mappings is obtained, which does not satisfy continuity and commutativity. The conditions are weaker than the usua...In this paper, some new existence and uniqueness of points of coincidence of weakly compatible pair of mappings is obtained, which does not satisfy continuity and commutativity. The conditions are weaker than the usual conditions in cone metric spaces.展开更多
The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.
We establish weak and strong convergence of Ishikawa type iterates of two pointwise asymptotic nonexpansive maps in a Hadamard space. For weak and strong convergence results, we drop “rate of convergence condition”,...We establish weak and strong convergence of Ishikawa type iterates of two pointwise asymptotic nonexpansive maps in a Hadamard space. For weak and strong convergence results, we drop “rate of convergence condition”, namely (Cn(x)-1)< to answer in the affirma-tive to the open question posed by Tan and Xu [1] even in a general setup.展开更多
Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 ： K → E be two weakly inward nonself asymptotically nonex...Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 ： K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence {kn^（i）} [1, ∞） （i = 1, 2）, and F ：= F（T1）∩ F（T2） ≠ 0. An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If E has also a Frechet differentiable norm or its dual E^＊ has Kadec-Klee property, then weak convergence theorems are obtained.展开更多
In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak （k, k＇） contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T1 ： Xγ...In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak （k, k＇） contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T1 ： XγY→ X and T2 ： XγY → Y be two operators which satisfy weak （k, k＇） contractive type condition. Using T1 and T2, we construct an operator T on X γ Y and show that T has a unique fixed point in a closed and bounded subset of X γY. We derive an iteration scheme converging to this unique fixed point of T. Conversely, using a weakly contractive mapping T, we construct a pair of mappings （T1, T2） satisfying weak （k, k＇） contractive type condition on X γ Y and from this pair, we also obtain two self mappings S1 and S2 on X and Y respectively with unique fixed points.展开更多
In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imp...In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imposed. This makes ns to deal with these kinds of mappings more easily. As obvious applications, some results in [3],[5],[7],[9],[10] are deepened and extended.展开更多
The aim of this paper is to prove common fixed point theorems for variants of weak compatible maps in a complex valued-metric space. In this paper, we generalize various known results in the literature using (CLRg) pr...The aim of this paper is to prove common fixed point theorems for variants of weak compatible maps in a complex valued-metric space. In this paper, we generalize various known results in the literature using (CLRg) property. The concept of (CLRg) does not require a more natural condition of closeness of range.展开更多
By using weakly compatible conditions of selfmapping pairs, we prove a com-mon fixed point theorem for six mappings in generalized complete metric spaces. An example is provided to support our result.
S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate b...S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i（A, Ω, p） is equal to nonzero, where i（A, Ω, p） is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2].展开更多
In this paper, we establish a common fixed pointtheorem for three pairs of self-mappings in fuzzy semi-metric space which improves and extends similar known results in the literature.
In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 4...In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.展开更多
文摘This paper is an attempt to investigate systematically fixed points of weakly inward maps by using some basic results from differential equations in Banach spaces. By investigating the Poincare operators for such differential equations, we establish a fixed point index theory for two classes of weakly inward maps.
文摘In this paper first we prove common fixed point theorems for compatible and weakly compatible maps. Secondly, we prove common fixed point theorems for weakly compatible maps along with property (E.A.) and (CLRg) property respectively.
文摘The notion of a G-symmetric space is introduced and the common fixed points for some pairs of occasionally weakly compatible maps satisfying some contractive conditions in a G-symmetric space are proved. The results extend and improve some results in literature.
文摘The aim of this paper is to establish some new common fixed point theorems for generalized contractive maps in fuzzy metric space by using property (E.A.), common property (E.A.), JCLRST property and CLRS property. Our results improve and extend the results of Chauhan et al. [1] and Sedghi et al. [2] besides several known results. We also furnish an illustrative example in support of our results.
基金Supported by National Natural Science Foundation of China (Grant Nos.1120141410971185+2 种基金11171162)the Natural Science Foundation of Fujian Province (Grant No.2012J05013)Training Programme Foundation for Excellent Youth Researching Talents of Fujian’s Universities (Grant No.JA13190)
文摘In this paper, we mainly discuss the images of certain spaces under closed sequencecovering maps. It is showed that the property with a locally countable weak base is preserved by closed sequence-covering maps. And the following question is discussed： Are the closed sequence-covering images of spaces with a point-countable sn-network sn-first countable？
文摘Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.
基金Project supported by the National Natural Science Foundation of China (No. 10471113)the Natural Science Foundation of Chongqing Municipal Commission of Science and Technology (N0.2005BB2097)
文摘In this paper, we introduce the concepts of weakly R-KKM mappings, R- convex and R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan＇s matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature.
基金Research supported by NSFC (10471149)Special Fund of Mathematics Research of Natural Science Foundation of Hebei Province (07M003)Doctoral Foundation of Hebei Province Ministry of Education (B2004103).
文摘The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a useful inequality is obtained, which can be used to derive the self-improving regularity.
文摘In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.
基金Supported by the Fundamental Research Fund of Sichuan Provincial Science and Technology Department(2012JYZ019)
文摘In this paper, some new existence and uniqueness of points of coincidence of weakly compatible pair of mappings is obtained, which does not satisfy continuity and commutativity. The conditions are weaker than the usual conditions in cone metric spaces.
文摘The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.
文摘We establish weak and strong convergence of Ishikawa type iterates of two pointwise asymptotic nonexpansive maps in a Hadamard space. For weak and strong convergence results, we drop “rate of convergence condition”, namely (Cn(x)-1)< to answer in the affirma-tive to the open question posed by Tan and Xu [1] even in a general setup.
文摘Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 ： K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence {kn^（i）} [1, ∞） （i = 1, 2）, and F ：= F（T1）∩ F（T2） ≠ 0. An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If E has also a Frechet differentiable norm or its dual E^＊ has Kadec-Klee property, then weak convergence theorems are obtained.
文摘In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak （k, k＇） contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T1 ： XγY→ X and T2 ： XγY → Y be two operators which satisfy weak （k, k＇） contractive type condition. Using T1 and T2, we construct an operator T on X γ Y and show that T has a unique fixed point in a closed and bounded subset of X γY. We derive an iteration scheme converging to this unique fixed point of T. Conversely, using a weakly contractive mapping T, we construct a pair of mappings （T1, T2） satisfying weak （k, k＇） contractive type condition on X γ Y and from this pair, we also obtain two self mappings S1 and S2 on X and Y respectively with unique fixed points.
文摘In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imposed. This makes ns to deal with these kinds of mappings more easily. As obvious applications, some results in [3],[5],[7],[9],[10] are deepened and extended.
文摘The aim of this paper is to prove common fixed point theorems for variants of weak compatible maps in a complex valued-metric space. In this paper, we generalize various known results in the literature using (CLRg) property. The concept of (CLRg) does not require a more natural condition of closeness of range.
文摘By using weakly compatible conditions of selfmapping pairs, we prove a com-mon fixed point theorem for six mappings in generalized complete metric spaces. An example is provided to support our result.
基金Supported in part by the Foundations of Education Ministry, Anhui Province, China (No: KJ2008A028)Education Ministry, Hubei Province, China (No: D20102502)
文摘S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i（A, Ω, p） is equal to nonzero, where i（A, Ω, p） is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2].
文摘In this paper, we establish a common fixed pointtheorem for three pairs of self-mappings in fuzzy semi-metric space which improves and extends similar known results in the literature.
文摘In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.
