In this paper, we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-C-non-expansive mappings and the set of solutions of an equilibrium problem. We establis...In this paper, we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-C-non-expansive mappings and the set of solutions of an equilibrium problem. We establish strong convergence theorems of common elements in uniformly smooth and strictly convex Banach spaces with the property （K）.展开更多
Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dyn...Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.展开更多
Every complete metric linear space is a K-space.A non-completenormed space can be a K-space.And non-metrizable K-spaces exist.A series ofbasic results on complete metric linear spaces Can be generalized to K-spaces.Fo...Every complete metric linear space is a K-space.A non-completenormed space can be a K-space.And non-metrizable K-spaces exist.A series ofbasic results on complete metric linear spaces Can be generalized to K-spaces.Forexample,every bounded linear operator from a K-space into a locally convex spaceis sequentially continuous;every bounded semi-norm on a K-space is sequentiallycontinuous and,therefore,piecewise separable;a.C-sequeatial K-space is both bar-relled and bornological;the family of sequentially continuous linear functionals ona K-space is weak sequentially complete.展开更多
This paper is concerned with the convergence rates of ergodic limits and approximation for regularized resolvent families for a linear Volterra integral equation. The results contain C 0-semigroups, cosine operator fu...This paper is concerned with the convergence rates of ergodic limits and approximation for regularized resolvent families for a linear Volterra integral equation. The results contain C 0-semigroups, cosine operator functions and α-times integrated resolvent family as special cases.展开更多
In this paper we introduce a generalization of Bernstein polynomials based on q calculus. With the help of Bohman-Korovkin type theorem, we obtain A-statistical approximation properties of these operators. Also, by us...In this paper we introduce a generalization of Bernstein polynomials based on q calculus. With the help of Bohman-Korovkin type theorem, we obtain A-statistical approximation properties of these operators. Also, by using the Modulus of continuity and Lipschitz class, the statistical rate of convergence is established. We also gives the rate of A-statistical convergence by means of Peetre＇s type K-functional. At last, approximation properties of a rth order generalization of these operators is discussed.展开更多
基金Supported by the National Natural Science Foundation of China (No. 10771050)Scientific Research Program Funded by Shaanxi Provincial Education Department (No. 11JK0486)
文摘In this paper, we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-C-non-expansive mappings and the set of solutions of an equilibrium problem. We establish strong convergence theorems of common elements in uniformly smooth and strictly convex Banach spaces with the property （K）.
文摘Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research.The concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space.In fact,It is a generalization by replacing the set of real numbers with a C^(∗)-algebra.After that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric spaces.Very recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case.In this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this setting.To support our main results,we also furnish some exampleswhichdemonstrate theutility of ourmainresult.Finally,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.
文摘Every complete metric linear space is a K-space.A non-completenormed space can be a K-space.And non-metrizable K-spaces exist.A series ofbasic results on complete metric linear spaces Can be generalized to K-spaces.Forexample,every bounded linear operator from a K-space into a locally convex spaceis sequentially continuous;every bounded semi-norm on a K-space is sequentiallycontinuous and,therefore,piecewise separable;a.C-sequeatial K-space is both bar-relled and bornological;the family of sequentially continuous linear functionals ona K-space is weak sequentially complete.
基金Supported by the National Natural Science Foundation of China(10231060,10501024)the Specialized Research Fund of Doc-toral Program of Higher Education of China(20040319003)+1 种基金the Natural Science Fund of Jiangsu Province(BK2006214)the Key Subject Fund of Nanjing Normal University
基金This project is supported by the Special Funds for Major Specialties of Shanghai Education Committee and the Natural Foundation ofShanghai City.
文摘This paper is concerned with the convergence rates of ergodic limits and approximation for regularized resolvent families for a linear Volterra integral equation. The results contain C 0-semigroups, cosine operator functions and α-times integrated resolvent family as special cases.
文摘In this paper we introduce a generalization of Bernstein polynomials based on q calculus. With the help of Bohman-Korovkin type theorem, we obtain A-statistical approximation properties of these operators. Also, by using the Modulus of continuity and Lipschitz class, the statistical rate of convergence is established. We also gives the rate of A-statistical convergence by means of Peetre＇s type K-functional. At last, approximation properties of a rth order generalization of these operators is discussed.
