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Equilibrium problems with generalized monotone mapping and its applications
Author(s) -
Liu Zhenhai,
Zeng Shengda
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3471
Subject(s) - mathematics , monotone polygon , constraint (computer aided design) , regular polygon , set (abstract data type) , fixed point theorem , pure mathematics , convex set , point (geometry) , mathematical economics , mathematical optimization , convex optimization , geometry , computer science , programming language
In this paper, we deal with invex equilibrium problems (IEPs for short). When the constraint set is compact convex, an existence result of solutions is obtained by Schauder's fixed point theorem. If the constraint set is closed invex, we introduce the concept of relaxed α – η pseudomonotone mappings and prove some existence results of solutions for the (IEPs), which extend and generalize several well‐known results in many respects. Moreover, we present that if the IEPs are applied to hemivariational inequalities problems, the conditions can be weakened. Copyright © 2015 John Wiley & Sons, Ltd.