Remarks on Caristi’s Fixed Point Theorem
نویسنده
چکیده
In this work, we give a characterization of the existence of minimal elements in partially ordered sets in terms of fixed point of multivalued maps. This characterization shows that the assumptions in Caristi’s fixed point theorem can, a priori, be weakened. Finally, we discuss Kirk’s problem on an extension of Caristi’s theorem and prove a new positive result which illustrates the weakening mentioned before.
منابع مشابه
Remarks on the Paper ``Coupled Fixed Point Theorems for Single-Valued Operators in b-Metric Spaces''
In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...
متن کاملSome Generalizations of Caristi’s Fixed Point Theorem with Applications
In this paper, we prove some generalizations of Caristi’s fixed point theorem, and then we give applications to Ekeland’s variational principle and maximal element theorem. Mathematics Subject Classification: 47H10, 54H25
متن کاملSome applications of Caristi’s fixed point theorem in metric spaces
*Correspondence: [email protected] 1Young Researcher and Elite Club, Arak-Branch, Islamic Azad University, Arak, Iran Full list of author information is available at the end of the article Abstract In this work, partial answers to Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s conjectures are presented via a light version of Caristi’s fixed point theorem. Moreover, we introduce th...
متن کاملOn the existence of minimal elements in partially ordered sets
In this work, we give a characterization of the existence of minimal elements in partially ordered sets in terms of fixed point type statement. This characterization shows that the assumptions in Caristi’s fixed point theorem can, a priori, be weakened. Finally, we give a negative answer to Kirk’s problem on an extension of Caristi’s result.
متن کاملCaristi Type Coincidence Point Theorem in Topological Spaces
The paper is concerned with a very general version of Caristi’s coincidence theorem, in topological spaces (X, τ) satisfying some completeness conditions with respect to a function p : X ×X → [0,∞), and having as consequence Caristi’s fixed point theorem. The general result is applied to various concrete situations quasi-metric spaces, bornological spaces to obtain versions of Ekeland’s variati...
متن کامل