Paper Title:

A Self-adaptive Subgradient Extragradient Algorithm for Variational Inequality Problems and Fixed Point Problems in Banach Spaces

Author(s):

F. U. Ogbuisi

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.

Department of Mathematics,
University of Nigeria, Nsukka,
Nigeria.
E-mail: ferdinard.ogbuisi@unn.edu.ng fudochukwu@yahoo.com

Abstract:

In this paper, we propose and analyze a type of subgradient extragradient algorithm for the approximation of a solution of variational inequality problem which is also a common fixed point of an infinite family of relatively nonexpansive mappings in 2-uniformly convex Banach spaces which are uniformly smooth. By using the generalized projection operator, we prove a strong convergence theorem which does not require the prior knowledge of the Lipschitz constant of cost operator. We further applied our result to constrained convex minimization problem, convex feasibility problem and infinite family of equilibrium problems. Our results improve and complement related results in 2-uniformly convex and uniformly smooth Banach spaces and Hilbert spaces.

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