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Existence results of the system of generalized variational inequalities with multi-valued mappings

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this article, we study a generalized variational inequality problem with multi-valued mappings over product sets and the system of generalized variational inequalities with multi-valued mappings which are equivalent problems. By developing the idea of generalized densely relatively pseudomonotone mappings, and by using well-known Fan-KKM theorem and fixed point theorem, we prove existence results of our problem. We construct an example of generalized Nash equilibrium problem in the context of our problem, and as an application of our results, we establish an existence of coincident point result.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    Mijanur Rahaman & Rais Ahmad

  2. Department of Mathematical Sciences, B.G.S.B. University, Rajouri, J&K, 185234, India

    Prinkya Gupta & Javid Iqbal

Authors
  1. Mijanur Rahaman
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  2. Prinkya Gupta
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  3. Javid Iqbal
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  4. Rais Ahmad
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Correspondence to Mijanur Rahaman.

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Rahaman, M., Gupta, P., Iqbal, J. et al. Existence results of the system of generalized variational inequalities with multi-valued mappings. RACSAM 113, 119–129 (2019). https://doi.org/10.1007/s13398-017-0457-9

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  • DOI: https://doi.org/10.1007/s13398-017-0457-9

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