In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich a...In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated withSλand consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations.We also establish certain interesting examples to illustrate the usability of our results.展开更多
In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the compl...In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces.We consider examples to illustrate the validity of the obtained result.展开更多
The focusofourwork is on themost recent results infixedpoint theoryrelated tocontractivemappings.Wedescribe variants of(s,q,φ,F)-contractions that expand,supplement and unify an important work widely discussed in the...The focusofourwork is on themost recent results infixedpoint theoryrelated tocontractivemappings.Wedescribe variants of(s,q,φ,F)-contractions that expand,supplement and unify an important work widely discussed in the literature,based on existing classes of interpolative and F-contractions.In particular,a large class of contractions in terms of s,q,φand F for both linear and nonlinear contractions are defined in the framework of b-metric-like spaces.The main result in our paper is that(s,q,φ,F)-g-weak contractions have a fixed point in b-metric-like spaces if function F or the specified contraction is continuous.As an application of our results,we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations.展开更多
In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged ...In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.展开更多
This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the correspo...This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.展开更多
In this paper,the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced.The fixed point theorems satisfying generalized contractive conditions are obtained,without appealing to c...In this paper,the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced.The fixed point theorems satisfying generalized contractive conditions are obtained,without appealing to completeness of X or normality of the cone.The continuity of the mapping is relaxed.Furthermore,we prove that the completeness in cone metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X.These results greatly generalize several well-known comparable results in the literature.展开更多
In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assump...In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.展开更多
In this paper, we establish the existence and uniqueness of fixed points of operator , when n is an arbitrary positive integer and X is a partially ordered complete metric space. We have shown examples to verify our w...In this paper, we establish the existence and uniqueness of fixed points of operator , when n is an arbitrary positive integer and X is a partially ordered complete metric space. We have shown examples to verify our work. Our results generalize the recent fixed point theorems cited in [1]-[4] etc. and include several recent developments.展开更多
In this work, we introduce a few versions of Caristi’s fixed point theorems in G-cone metric spaces which extend Caristi’s fixed point theorems in metric spaces. Analogues of such fixed point theorems are proved in ...In this work, we introduce a few versions of Caristi’s fixed point theorems in G-cone metric spaces which extend Caristi’s fixed point theorems in metric spaces. Analogues of such fixed point theorems are proved in this space. Our work extends a good number of results in this area of research.展开更多
Let H_1, H_2, H_3 be real Hilbert spaces, let A : H_1→ H_3, B : H_2→ H_3 be two bounded linear operators. The split equality common fixed point problem(SECFP) in the infinite-dimensional Hilbert spaces introduced by...Let H_1, H_2, H_3 be real Hilbert spaces, let A : H_1→ H_3, B : H_2→ H_3 be two bounded linear operators. The split equality common fixed point problem(SECFP) in the infinite-dimensional Hilbert spaces introduced by Moudafi(Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis)is to find x ∈ F(U), y ∈ F(T) such that Ax = By,(1)where U : H_1→ H_1 and T : H_2→ H_2 are two nonlinear operators with nonempty fixed point sets F(U) = {x ∈ H_1: Ux = x} and F(T) = {x ∈ H_2: Tx = x}. Note that,by taking B = I and H_2= H_3 in(1), we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP(1) of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP(1) governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.展开更多
A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed...A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems.展开更多
In this paper, we present a new fixed point theorem in L-convex spaces and apply it to obtain a maximal element theorem, a variational inequality and a saddle point theorem in L-convex spaces.
In this paper,we study the di erence equation a1(z)f(z+1)+a0(z)f(z)=0;where a1(z)and a0(z)are entire functions of nite order.Under some conditions,we obtain some properties,such as xed points,zeros etc.,of the di eren...In this paper,we study the di erence equation a1(z)f(z+1)+a0(z)f(z)=0;where a1(z)and a0(z)are entire functions of nite order.Under some conditions,we obtain some properties,such as xed points,zeros etc.,of the di erences and forward di erences of meromorphic solutions of the above equation.展开更多
In order to develop and improve the fixed point theorems in cone metric spaces, some new fixed point theorems are presented for two mappings in cone metric spaces which satisfy contractive conditions, where the cone i...In order to develop and improve the fixed point theorems in cone metric spaces, some new fixed point theorems are presented for two mappings in cone metric spaces which satisfy contractive conditions, where the cone is not necessarily normal. Our results generalize fixed point theorems of Abbas, Jungck and Stojan Radenovi in cone metric spaces.展开更多
We prove some fixed point theorems. As applications we obtain Brosowski - Meinardus type theorems on invariant approximations on a class of nonconvex sets in locally bounded topological vector spaces.
Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition fo...Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.展开更多
Let be a normal completely positive map with Kraus operators . An operator X is said to be a fixed point of , if . Let be the fixed points set of . In this paper, fixed points of are considered for , where means j-pow...Let be a normal completely positive map with Kraus operators . An operator X is said to be a fixed point of , if . Let be the fixed points set of . In this paper, fixed points of are considered for , where means j-power of . We obtain that and for integral when A is self-adjoint and commutable. Moreover, holds under certain condition.展开更多
In this article, we establish some common fixed point theorems for two pairs of weakly compatible mappings with (E. A.) and (CLR) property in dislocated metric space which generalize and extend some similar results in...In this article, we establish some common fixed point theorems for two pairs of weakly compatible mappings with (E. A.) and (CLR) property in dislocated metric space which generalize and extend some similar results in the literature.展开更多
In this article, we establish a common fixed point theorem satisfying integral type contractive condition for two pairs of weakly compatible mappings with E. A. property and also generalize Theorem (2) of B.E. Rhoades...In this article, we establish a common fixed point theorem satisfying integral type contractive condition for two pairs of weakly compatible mappings with E. A. property and also generalize Theorem (2) of B.E. Rhoades [1] in dislocated metric space.展开更多
In this paper,we introduce the concept of comparable T-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a com...In this paper,we introduce the concept of comparable T-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a comparable T-complete partially ordered Menger PM-space.We obtain some new results which generalize many known ones in the literature.Moreover,we derive some consequent results and give an example to illustrate our main result.展开更多
文摘In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated withSλand consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations.We also establish certain interesting examples to illustrate the usability of our results.
文摘In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces.We consider examples to illustrate the validity of the obtained result.
文摘The focusofourwork is on themost recent results infixedpoint theoryrelated tocontractivemappings.Wedescribe variants of(s,q,φ,F)-contractions that expand,supplement and unify an important work widely discussed in the literature,based on existing classes of interpolative and F-contractions.In particular,a large class of contractions in terms of s,q,φand F for both linear and nonlinear contractions are defined in the framework of b-metric-like spaces.The main result in our paper is that(s,q,φ,F)-g-weak contractions have a fixed point in b-metric-like spaces if function F or the specified contraction is continuous.As an application of our results,we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations.
文摘In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.
基金by Dr Kemp from National Mathematics and Science College.
文摘This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.
基金Supported by the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities'Association(202101BA070001-045)the Science and Technology Development Fund,Macao SAR(0019/2021/A1).
文摘In this paper,the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced.The fixed point theorems satisfying generalized contractive conditions are obtained,without appealing to completeness of X or normality of the cone.The continuity of the mapping is relaxed.Furthermore,we prove that the completeness in cone metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X.These results greatly generalize several well-known comparable results in the literature.
基金supported by the Foundation of Education Ministry,Hubei Province,China(Q20122203)
文摘In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.
文摘In this paper, we establish the existence and uniqueness of fixed points of operator , when n is an arbitrary positive integer and X is a partially ordered complete metric space. We have shown examples to verify our work. Our results generalize the recent fixed point theorems cited in [1]-[4] etc. and include several recent developments.
文摘In this work, we introduce a few versions of Caristi’s fixed point theorems in G-cone metric spaces which extend Caristi’s fixed point theorems in metric spaces. Analogues of such fixed point theorems are proved in this space. Our work extends a good number of results in this area of research.
基金supported by National Natural Science Foundation of China(61503385)Fundamental Research Funds for the Central Universities of China(3122016L002)
文摘Let H_1, H_2, H_3 be real Hilbert spaces, let A : H_1→ H_3, B : H_2→ H_3 be two bounded linear operators. The split equality common fixed point problem(SECFP) in the infinite-dimensional Hilbert spaces introduced by Moudafi(Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis)is to find x ∈ F(U), y ∈ F(T) such that Ax = By,(1)where U : H_1→ H_1 and T : H_2→ H_2 are two nonlinear operators with nonempty fixed point sets F(U) = {x ∈ H_1: Ux = x} and F(T) = {x ∈ H_2: Tx = x}. Note that,by taking B = I and H_2= H_3 in(1), we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP(1) of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP(1) governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.
文摘A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems.
基金Foundation item： Supported by the Natural Science Foundation of Guizhou Province（J2011]2093）
文摘In this paper, we present a new fixed point theorem in L-convex spaces and apply it to obtain a maximal element theorem, a variational inequality and a saddle point theorem in L-convex spaces.
基金National Natural Science Foundation of China(11801110,11771090,11761035,11871260).
文摘In this paper,we study the di erence equation a1(z)f(z+1)+a0(z)f(z)=0;where a1(z)and a0(z)are entire functions of nite order.Under some conditions,we obtain some properties,such as xed points,zeros etc.,of the di erences and forward di erences of meromorphic solutions of the above equation.
基金Foundation item： Supported by the NNSF of China（10771212） Supported by the Natural Science Foundation of Xuzhou Normal University（09KLB03）
文摘In order to develop and improve the fixed point theorems in cone metric spaces, some new fixed point theorems are presented for two mappings in cone metric spaces which satisfy contractive conditions, where the cone is not necessarily normal. Our results generalize fixed point theorems of Abbas, Jungck and Stojan Radenovi in cone metric spaces.
文摘We prove some fixed point theorems. As applications we obtain Brosowski - Meinardus type theorems on invariant approximations on a class of nonconvex sets in locally bounded topological vector spaces.
基金Supported by the National Natural Science Foundation of China（11271293）
文摘Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.
文摘Let be a normal completely positive map with Kraus operators . An operator X is said to be a fixed point of , if . Let be the fixed points set of . In this paper, fixed points of are considered for , where means j-power of . We obtain that and for integral when A is self-adjoint and commutable. Moreover, holds under certain condition.
文摘In this article, we establish some common fixed point theorems for two pairs of weakly compatible mappings with (E. A.) and (CLR) property in dislocated metric space which generalize and extend some similar results in the literature.
文摘In this article, we establish a common fixed point theorem satisfying integral type contractive condition for two pairs of weakly compatible mappings with E. A. property and also generalize Theorem (2) of B.E. Rhoades [1] in dislocated metric space.
基金Supported by the National Natural Science Foundation of China(12161056,11701259,11771198)Natural Science Foundation of Jiangxi Province of China(20202BAB201001).
文摘In this paper,we introduce the concept of comparable T-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a comparable T-complete partially ordered Menger PM-space.We obtain some new results which generalize many known ones in the literature.Moreover,we derive some consequent results and give an example to illustrate our main result.
