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Article

New Generalized Ekeland’s Variational Principle, Critical Point Theorems and Common Fuzzy Fixed Point Theorems Induced by Lin-Du’s Abstract Maximal Element Principle

by 1 and 2,*
1
School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
2
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
*
Author to whom correspondence should be addressed.
Axioms 2021, 10(1), 11; https://doi.org/10.3390/axioms10010011
Received: 19 December 2020 / Revised: 15 January 2021 / Accepted: 17 January 2021 / Published: 20 January 2021
(This article belongs to the Special Issue Nonlinear Analysis and Optimization with Applications)
In this paper, by applying the abstract maximal element principle of Lin and Du, we present some new existence theorems related with critical point theorem, maximal element theorem, generalized Ekeland’s variational principle and common (fuzzy) fixed point theorem for essential distances. View Full-Text
Keywords: maximal element; fixed point; sizing-up function; μ-bounded quasi-ordered set; critical point; fuzzy mapping; Ekeland’s variational principle; Caristi’s fixed point theorem; Takahashi’s nonconvex minimization theorem; essential distance maximal element; fixed point; sizing-up function; μ-bounded quasi-ordered set; critical point; fuzzy mapping; Ekeland’s variational principle; Caristi’s fixed point theorem; Takahashi’s nonconvex minimization theorem; essential distance
MDPI and ACS Style

Zhao, J.; Du, W.-S. New Generalized Ekeland’s Variational Principle, Critical Point Theorems and Common Fuzzy Fixed Point Theorems Induced by Lin-Du’s Abstract Maximal Element Principle. Axioms 2021, 10, 11. https://doi.org/10.3390/axioms10010011

AMA Style

Zhao J, Du W-S. New Generalized Ekeland’s Variational Principle, Critical Point Theorems and Common Fuzzy Fixed Point Theorems Induced by Lin-Du’s Abstract Maximal Element Principle. Axioms. 2021; 10(1):11. https://doi.org/10.3390/axioms10010011

Chicago/Turabian Style

Zhao, Junjian; Du, Wei-Shih. 2021. "New Generalized Ekeland’s Variational Principle, Critical Point Theorems and Common Fuzzy Fixed Point Theorems Induced by Lin-Du’s Abstract Maximal Element Principle" Axioms 10, no. 1: 11. https://doi.org/10.3390/axioms10010011

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