On Mann-type accelerated projection methods for pseudomonotone variational inequalities and common fixed points in Banach spaces
Lu-Chuan Ceng, Yeong‐Cheng Liou, Tzu-Chien Yin
Abstract
<abstract><p>In this paper, we investigate two Mann-type accelerated projection procedures with line search method for solving the pseudomonotone variational inequality (VIP) and the common fixed-point problem (CFPP) of finitely many Bregman relatively nonexpansive mappings and a Bregman relatively asymptotically nonexpansive mapping in $ p $-uniformly convex and uniformly smooth Banach spaces. Under mild conditions, we show weak and strong convergence of the proposed algorithms to a common solution of the VIP and CFPP, respectively.</p></abstract>
Topics & Concepts
Variational inequalityBanach spaceMathematicsFixed pointConvergence (economics)Projection (relational algebra)Type (biology)Regular polygonPure mathematicsApplied mathematicsMathematical analysisAlgorithmGeometryBiologyEconomic growthEconomicsEcologyOptimization and Variational AnalysisAdvanced Optimization Algorithms ResearchFixed Point Theorems Analysis