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A Common Fixed Point Theorem with Applications

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Abstract

In this paper, we establish a common fixed point theorem for a family of self set-valued mappings on a compact and convex set in a locally convex topological vector space. As applications, we obtain an existence theorem of solutions for a variational inequality of Stampacchia type and some Ky Fan-type minimax inequalities.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University—Kingsville, 700 University Blvd., Kingsville, TX, 78363-8202, USA

    R. P. Agarwal

  2. Department of Mathematics, University of Oradea, 410087, Oradea, Romania

    M. Balaj

  3. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    D. O’Regan

Authors
  1. R. P. Agarwal
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  2. M. Balaj
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  3. D. O’Regan
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Corresponding author

Correspondence to R. P. Agarwal.

Additional information

Communicated by Qamrul Hasan Ansari.

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Agarwal, R.P., Balaj, M. & O’Regan, D. A Common Fixed Point Theorem with Applications. J Optim Theory Appl 163, 482–490 (2014). https://doi.org/10.1007/s10957-013-0490-6

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  • DOI: https://doi.org/10.1007/s10957-013-0490-6

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