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Generalized Variational Relation Problems with Applications

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Abstract

In this paper, we first obtain an existence theorem of the solutions for a variational relation problem. An existence theorem for a variational inclusion problem, a KKM theorem and an extension of the well know Ky Fan inequality will be established, as particular cases. Some applications concerning a saddle point problem with constraints, existence of a common fixed point for two mappings and an optimization problem with constraints, will be given in the last section of the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Oradea, Oradea, Romania

    M. Balaj

  2. Department of Mathematics, National Changhua University of Education, Changhua, Taiwan

    L. J. Lin

Authors
  1. M. Balaj
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  2. L. J. Lin
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Correspondence to L. J. Lin.

Additional information

Communicated by J.P. Crouzeix.

The authors would like to thank the referees for their suggestions, which have improved the presentation of the paper.

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Balaj, M., Lin, L.J. Generalized Variational Relation Problems with Applications. J Optim Theory Appl 148, 1–13 (2011). https://doi.org/10.1007/s10957-010-9741-y

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