Convergence theorems for a countable family of Lipschitzian mappings

Iterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

Convergence Theorems For Two Finite Families of Uniformly L-Lipschitzian Mappings

A Hybrid Method for a Countable Family of Lipschitz Generalized Asymptotically Quasi-nonexpansive Mappings and an Equilibrium Problem

In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W -mappings of a countable family of ...

On the Convergence Theorems for a Countable Family of Lipschitzian Pseudocontraction Mappings in Banach Spaces

The purpose of this paper is to study the weak and strong convergence theorems of the implicit iteration process for a countable family of Lipschitzian pseudocontraction mappings in Banach spaces. The results presented in this paper extend and improve some recent results announced by some authors.

Strong Convergence Theorems for Countable Lipschitzian Mappings and Its Applications in Equilibrium and Optimization Problems

The purpose of this paper is to propose a modified hybrid method in mathematical programming and to obtain some strong convergence theorems for common fixed points of a countable family of Lipschitzian mappings. Further, we apply our results to solve the equilibrium and optimization problems. The results of this paper improved and extended the results of W. Nilsrakoo and S. Saejung 2008 and som...

Strong convergence results for fixed points of nearly weak uniformly L-Lipschitzian mappings of I-Dominated mappings

In this paper, we prove strong convergence results for a modified Mann iterative process for a new class of I- nearly weak uniformly L-Lipschitzian mappings in a real Banach space. The class of I-nearly weak uniformly L-Lipschitzian mappings is an interesting generalization of the class of nearly weak uniformly L-Lipschitzian mappings which inturn is a generalization of the class of nearly unif...