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Generalized equilibrium problem with mixed relaxed monotonicity.

Haider Abbas Rizvi1, Adem Kılıçman2, Rais Ahmad1

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

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|August 15, 2014
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Summary
This summary is machine-generated.

Researchers introduced mixed relaxed α-β-monotonicity, a more general concept than existing monotonicities. This advancement, combined with KKM-theory, aids in solving generalized equilibrium problems.

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Area of Science:

  • Mathematical Analysis
  • Optimization Theory

Background:

  • Monotonicity concepts are crucial in various mathematical fields.
  • Existing monotonicity concepts have limitations in generality.

Purpose of the Study:

  • To introduce and define mixed relaxed α-β-monotonicity.
  • To establish the generality of this new concept.
  • To apply the new concept to solve generalized equilibrium problems.

Main Methods:

  • Extension of the concept of relaxed α-monotonicity.
  • Application of KKM-theory (Ky Fan's theorem).

Main Results:

  • The proposed mixed relaxed α-β-monotonicity is a generalization of existing monotonicity concepts.
  • A method for solving generalized equilibrium problems using the new concept and KKM-theory is presented.

Conclusions:

  • Mixed relaxed α-β-monotonicity offers a more flexible framework for analyzing equilibrium problems.
  • The study provides a novel approach to solving generalized equilibrium problems.