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Journal of Inequalities and Applications
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Applications of W. A. Kirk's fixed-point theorem to generalized nonlinear variational-like inequalities in reflexive Banach spaces

Journal of Inequalities and Applications volume 2005, Article number: 634163 (2005) Cite this article

Abstract

We introduce and study a new class of generalized nonlinear variational-like inequalities, which includes these variational inequalities and variational-like inequalities due to Bose, Cubiotti, Dien, Ding, Ding and Tarafdar, Noor, Parida, Sahoo, and Kumar, and Yao, and others as special cases. By applying Kirk's fixed-point theorem and Ding-Tan minimax inequality, we establish the existence theorems of solutions for the generalized nonlinear variational-like inequalities in reflexive Banach spaces.

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Authors and Affiliations

  1. Department of Mathematics, Liaoning Normal University, Liaoning, Dalian, 116029, China

    Zeqing Liu

  2. Department of Applied Mathematics, College of Natural Sciences, Changwon National University, Kyongnam, Changwon, 641-773, Korea

    Jeong Sheok Ume

  3. Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju, 660-701, Korea

    Shin Min Kang

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  1. Zeqing Liu
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  2. Jeong Sheok Ume
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  3. Shin Min Kang
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Correspondence to Zeqing Liu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Liu, Z., Ume, J.S. & Kang, S.M. Applications of W. A. Kirk's fixed-point theorem to generalized nonlinear variational-like inequalities in reflexive Banach spaces. J Inequal Appl 2005, 634163 (2005). https://doi.org/10.1155/JIA.2005.251

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  • DOI: https://doi.org/10.1155/JIA.2005.251