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Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings
Authors:Habtu Zegeye  Eric U. Ofoedu  Naseer Shahzad
Affiliation:a Bahir Dar University, P.O. Box 859, Bahir Dar, Ethiopia
b Department of Mathematics, Nnamdi Azikiwe University, P.M.B. 5025, Awka, Anambra State, Nigeria
c Department of Mathematics, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Abstract:In this paper, we introduce an iterative process which converges strongly to a common element of set of common fixed points of countably infinite family of closed relatively quasi- nonexpansive mappings, the solution set of generalized equilibrium problem and the solution set of the variational inequality problem for a γ-inverse strongly monotone mapping in Banach spaces. Our theorems improve, generalize, unify and extend several results recently announced.
Keywords:Equilibrium problem     mmlsi2"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0096300310002420&  _mathId=si2.gif&  _pii=S0096300310002420&  _issn=00963003&  _acct=C000051805&  _version=1&  _userid=1154080&  md5=323b55bb31c892aab10e29bfb18ca7f7')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >γ-inverse strongly monotone mappings   Monotone mappings   Strong convergence   Strongly monotone mappings   Variational inequality problems
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