Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions
نویسندگان
چکیده
This paper concerns common fixed points for a finite family of hemicontractions or a finite family of strict pseudocontractions on uniformly convex Banach spaces. By introducing a new iteration process with error term, we obtain sufficient and necessary conditions, as well as sufficient conditions, for the existence of a fixed point. As one will see, we derive these strong convergence theorems in uniformly convex Banach spaces and without any requirement of the compactness on the domain of the mapping. The results given in this paper extend some previous theorems.
منابع مشابه
Approximating fixed points for nonexpansive mappings and generalized mixed equilibrium problems in Banach spaces
We introduce a new iterative scheme for nding a common elementof the solutions set of a generalized mixed equilibrium problem and the xedpoints set of an innitely countable family of nonexpansive mappings in a Banachspace setting. Strong convergence theorems of the proposed iterative scheme arealso established by the generalized projection method. Our results generalize thecorresponding results...
متن کاملAn Iterative Scheme for Generalized Equilibrium, Variational Inequality and Fixed Point Problems Based on the Extragradient Method
The problem ofgeneralized equilibrium problem is very general in the different subjects .Optimization problems, variational inequalities, Nash equilibrium problem and minimax problems are as special cases of generalized equilibrium problem. The purpose of this paper is to investigate the problem of approximating a common element of the set of generalized equilibrium problem, variational inequal...
متن کاملNew iteration process for approximating fixed points in Banach spaces
The object of this paper is to present a new iteration process. We will show that our process is faster than the known recent iterative schemes. We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings. We also present a numerical example for proving the rate of convergence of our res...
متن کاملA new one-step iterative process for approximating common fixed points of a countable family of quasi-nonexpansive multi-valued mappings in CAT(0) spaces
In this paper, we propose a new one-step iterative process for a countable family of quasi-nonexpansive multi-valued mappings in a CAT(0) space. We also prove strong and $Delta$-convergence theorems of the proposed iterative process under some control conditions. Our main results extend and generalize many results in the literature.
متن کامل