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Existence theorems for perturbed variational inequalities in Banach spaces

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Abstract

The aim of this paper is to establish existence and boundedness theorems for perturbed variational inequalities defined by a set-valued mapping without any kind of monotonicity in Banach spaces. The first result is shown that if a coercivity condition holds, then the solution set of a variational inequality perturbed along a direction is nonempty and uniformly bounded. Second, by employing the Minty variational inequalities perturbed by a nonlinear mapping without monotonicity, we prove the boundedness result for the corresponding perturbed variational inequalities under a kind of coercivity condition.

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Authors and Affiliations

  1. School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan, 610066, China

    Min Wang

  2. School of Mathematics and Physics, Mianyang Teachers’ College, Mianyang, Sichuan, 621050, China

    Min Wang

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  1. Min Wang
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Correspondence to Min Wang.

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Wang, M. Existence theorems for perturbed variational inequalities in Banach spaces. J. Fixed Point Theory Appl. 20, 55 (2018). https://doi.org/10.1007/s11784-018-0536-3

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  • DOI: https://doi.org/10.1007/s11784-018-0536-3

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