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From an abstract maximal element principle to optimization problems, stationary point theorems and common fixed point theorems

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Abstract

In this paper, we first establish an existence theorem related with intersection theorem, maximal element theorem and common fixed point theorem for multivalued maps by applying an abstract maximal element principle proved by Lin and Du. Some new stationary point theorems, minimization problems, new fixed point theorems and a system of nonconvex equilibrium theorem are also given.

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Authors and Affiliations

  1. Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan

    Lai-Jiu Lin

  2. Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 802, Taiwan

    Wei-Shih Du

Authors
  1. Lai-Jiu Lin
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  2. Wei-Shih Du
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Correspondence to Lai-Jiu Lin.

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Lin, LJ., Du, WS. From an abstract maximal element principle to optimization problems, stationary point theorems and common fixed point theorems. J Glob Optim 46, 261–271 (2010). https://doi.org/10.1007/s10898-009-9423-1

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  • DOI: https://doi.org/10.1007/s10898-009-9423-1

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