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
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
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive ...In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.展开更多
Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-value...Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.展开更多
We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We ...We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We prove mean square convergence and convergence almost sure (a.s.) of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate in degenerate and non-degenerate cases. Previously the stochastic approximation algorithms were studied mainly for optimization problems.展开更多
This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Ca...This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4].展开更多
In this paper, we establish a fixed point theorem for set-valued mapping on a topological vector space without ＂local convexity＂. And we also establish some generalized Ky Fan＇s minimax inequalities for set-value v...In this paper, we establish a fixed point theorem for set-valued mapping on a topological vector space without ＂local convexity＂. And we also establish some generalized Ky Fan＇s minimax inequalities for set-value vector mappings, which are the generalization of some previous results.展开更多
This article introduces the Fiber-to-the-World total solution, a fixed access network solution launched by ZTE Corporation. The ZXA10-MSAN system, an important part of the solution, is presented. The ZXMSG 5200/5600 a...This article introduces the Fiber-to-the-World total solution, a fixed access network solution launched by ZTE Corporation. The ZXA10-MSAN system, an important part of the solution, is presented. The ZXMSG 5200/5600 access gateway system, the updated version of ZXA10-MSAN, is also described. Moreover, ZXPON, the passive optical network system, is mentioned. The wide application of the solution is demonstrated by three application cases in the end.展开更多
In this paper the existence of solutions of a boundary value problem forimpulsively differential equations that is difficult to solve by the upper and lowersolution method will be proved by means of Schauder’s fixed ...In this paper the existence of solutions of a boundary value problem forimpulsively differential equations that is difficult to solve by the upper and lowersolution method will be proved by means of Schauder’s fixed point theorem,whichimproves some existing results.展开更多
In this work, we will discuss Caristi’s fixed point theorem for mapping results introduced in the setting of normed spaces. This work is a generalization of the classical Caristi’s fixed point theorem. Also, Caristi...In this work, we will discuss Caristi’s fixed point theorem for mapping results introduced in the setting of normed spaces. This work is a generalization of the classical Caristi’s fixed point theorem. Also, Caristi’s type of fixed points theorem was partial discussed in Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s results, we developed ideas that many known fixed point theorems can easily be derived from the Caristi theorem.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
During the Eighth Five-Year Planperiod, Shaanxi Province intensifiedthe restructuring of investment andmacro-control in fixed assets investment byimplementing the policy of "limiting totalamount, readjusting stru...During the Eighth Five-Year Planperiod, Shaanxi Province intensifiedthe restructuring of investment andmacro-control in fixed assets investment byimplementing the policy of "limiting totalamount, readjusting structure, rectifying orderand improving efficiency". The wholeprovince realized RMB 110 billion in fixedassets investment, (including RMB 86.5 billionby state-owned units, RMB 14.23 billionthrough loans from the construction bank,making up 16.5 percent), RMB 67 billionmore than in the Seventh Five-Year Planperiod, with an annual increase of 26.5 percent.Thanks to the support, a group of medium-to-large and key projects have been put展开更多
For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbation...For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions.展开更多
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.
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.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
基金supported by Università degli Studi di Palermo (Local University Project ex 60%)
文摘In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.
文摘Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.
文摘We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We prove mean square convergence and convergence almost sure (a.s.) of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate in degenerate and non-degenerate cases. Previously the stochastic approximation algorithms were studied mainly for optimization problems.
文摘This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4].
基金The NSF(9452902001003278,10452902001005845) of Guangdong Province
文摘In this paper, we establish a fixed point theorem for set-valued mapping on a topological vector space without ＂local convexity＂. And we also establish some generalized Ky Fan＇s minimax inequalities for set-value vector mappings, which are the generalization of some previous results.
文摘This article introduces the Fiber-to-the-World total solution, a fixed access network solution launched by ZTE Corporation. The ZXA10-MSAN system, an important part of the solution, is presented. The ZXMSG 5200/5600 access gateway system, the updated version of ZXA10-MSAN, is also described. Moreover, ZXPON, the passive optical network system, is mentioned. The wide application of the solution is demonstrated by three application cases in the end.
文摘In this paper the existence of solutions of a boundary value problem forimpulsively differential equations that is difficult to solve by the upper and lowersolution method will be proved by means of Schauder’s fixed point theorem,whichimproves some existing results.
文摘In this work, we will discuss Caristi’s fixed point theorem for mapping results introduced in the setting of normed spaces. This work is a generalization of the classical Caristi’s fixed point theorem. Also, Caristi’s type of fixed points theorem was partial discussed in Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s results, we developed ideas that many known fixed point theorems can easily be derived from the Caristi theorem.
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.
文摘During the Eighth Five-Year Planperiod, Shaanxi Province intensifiedthe restructuring of investment andmacro-control in fixed assets investment byimplementing the policy of "limiting totalamount, readjusting structure, rectifying orderand improving efficiency". The wholeprovince realized RMB 110 billion in fixedassets investment, (including RMB 86.5 billionby state-owned units, RMB 14.23 billionthrough loans from the construction bank,making up 16.5 percent), RMB 67 billionmore than in the Seventh Five-Year Planperiod, with an annual increase of 26.5 percent.Thanks to the support, a group of medium-to-large and key projects have been put
文摘For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions.
