Convergence Theorems for Hierarchical Fixed Point Problems and Variational Inequalities

This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under certain approximate assumptions of mappings and parameters. As a special case, this projection method solves some quadratic minimization problem. It should be noted that the proposed method can be regarded as a generalized version of Wang et.al. [15], Ceng et. al. [14], Sahu [4] and many other authors.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1403.321

Strong Convergence Theorems for a Generalized Mixed Equilibrium Problem and a Family of Total Quasi--Asymptotically Nonexpansive Multivalued Mappings in Banach Spaces

The main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi--asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors

Approximating fixed point of({\lambda},{\rho})-firmly nonexpansive mappings in modular function spaces

In this paper, we first introduce an iterative process in modular function spaces and then extend the idea of a {\lambda}-firmly nonexpansive mapping from Banach spaces to modular function spaces. We call such mappings as ({\lambda},{\rho})-firmly nonexpansive mappings. We incorporate the two ideas to approximate fixed points of ({\lambda},{\rho})-firmly nonexpansive mappings using the above mentioned iterative process in modular function spaces. We give an example to validate our results

A von Neumann Alternating Method for Finding Common Solutions to Variational Inequalities

Modifying von Neumann's alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space.Comment: Nonlinear Analysis Series A: Theory, Methods & Applications, accepted for publicatio