TY - JOUR

T1 - An algorithm for finding a common point of the solutions of fixed point and variational inequality problems in Banach spaces

AU - Tufa, Abebe R.

AU - Zegeye, H.

PY - 2015/9/1

Y1 - 2015/9/1

N2 - Let C be a nonempty, closed and convex subset of a 2-uniformly convex and uniformly smooth real Banach space E. Let T: C→ C be relatively nonexpansive mapping and let Ai: C→ E* be Li-Lipschitz monotone mappings, for i = 1,2. In this paper, we introduce and study an iterative process for finding a common point of the fixed point set of a relatively nonexpansive mapping and the solution set of variational inequality problems for A1 and A2. Under some mild assumptions, we show that the proposed algorithm converges strongly to a point in F(T) ∩ VI(C, A1) ∩ VI(C, A2). Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

AB - Let C be a nonempty, closed and convex subset of a 2-uniformly convex and uniformly smooth real Banach space E. Let T: C→ C be relatively nonexpansive mapping and let Ai: C→ E* be Li-Lipschitz monotone mappings, for i = 1,2. In this paper, we introduce and study an iterative process for finding a common point of the fixed point set of a relatively nonexpansive mapping and the solution set of variational inequality problems for A1 and A2. Under some mild assumptions, we show that the proposed algorithm converges strongly to a point in F(T) ∩ VI(C, A1) ∩ VI(C, A2). Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

UR - http://www.scopus.com/inward/record.url?scp=85034664836&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034664836&partnerID=8YFLogxK

U2 - 10.1007/s40065-015-0130-0

DO - 10.1007/s40065-015-0130-0

M3 - Article

AN - SCOPUS:85034664836

VL - 4

SP - 199

EP - 213

JO - Arabian Journal of Mathematics

JF - Arabian Journal of Mathematics

SN - 2193-5343

IS - 3

ER -