Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.7.2023.3.04

Volume 7, Issue 3, 1 June 2023, Pages 381-396

 

Abstract. In this paper, a weighted set order relation given by the oriented distance function is introduced, which does not need any convexity and is applicable even the ordering cone has an empty interior. The Ekeland’s variational principle, Caristi’s fixed point theorem, and Takahashi’s minimization theorem associated with the introduced weighted set order relation are constructed, and the equivalences among them are deduced. As an application, the existence of solutions to a set optimization problem is examined to verify the validity of the results obtained.

 

How to Cite this Article:
W. Han, G. Yu, Ekeland’s variational principle with a scalarization type weighted set order relation, J. Nonlinear Var. Anal. 7 (2023), 381-396.