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In this paper we give a quasi-metric version of Caristi's fixed point theorem by using mw-distances. Our theorem generalizes a recent result obtained by Karapinar and Romaguera in [7]. [ABSTRACT FROM AUTHOR]

This paper brings forward the concept of Caristi type hybrid fixed point in MPM-space, by giving two hybrid fixed point theorems and two common hybrid fixed point theorems of sequences of set-valued mappings, the theorems improve and generalize the Caristi's fixed point and correspond to recent important results. [ABSTRACT FROM AUTHOR]

We solve a question posed by E. Karapinar, F. Khojasteh and Z.D. Mitrović in their paper "A Proposal for Revisiting Banach and Caristi Type Theorems in b-Metric Spaces". We also characterize the completeness of b-metric spaces with the help of a variant of the contractivity condition introduced by the authors in the aforementioned article. [ABSTRACT FROM AUTHOR]

In this paper, we study common fixed point properties for a family of mappings. We present the extensions of Caristi's fixed point theorem and Markov–Kakutani fixed point theorem for a family of set-valued mappings. [ABSTRACT FROM AUTHOR]

We extend Nadler's fixed point theorem to ν-generalized metric spaces. Through the proof of the above extension, we understand more deeply the mathematical structure of a ν-generalized metric space. In particular, we study the completeness of the space. We also improve Caristi's and Subrahmanyam's fixed point theorems in the space. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the famous Banach contraction principle and Caristi''s fixed point theorem are generalized to the case of multi-valued mappings. Our results are extensions of the well-known Nadler''s fixed point theorem [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475–487], as well as of some Caristi type theorems for multi-valued operators, see [N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177–188; J.P. Aubin, Optima and Equilibria. An Introduction to Nonlinear Analysis, Grad. Texts in Math., Springer-Verlag, Berlin, 1998, p. 17; S.S. Zhang, Q. Luo, Set-valued Caristi fixed point theorem and Ekeland''s variational principle, Appl. Math. Mech. 10 (2) (1989) 111–113 (in Chinese), English translation: Appl. Math. Mech. (English Ed.) 10 (2) (1989) 119–121], etc. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the generalized Caristi''s fixed point theorems proved by Bae [J. Math. Anal. Appl. 284 (2003) 690–697] and others. [Copyright &y& Elsevier]

We solve a question posed by E. Karapinar, F. Khojasteh and Z.D. Mitrović in their paper “A Proposal for Revisiting Banach and Caristi Type Theorems in b-Metric Spaces”. We also characterize the completeness of b-metric spaces with the help of a variant of the contractivity condition introduced by the authors in the aforementioned article.

In this paper we establish and prove a generalized variational principle for b-metric spaces. As a consequence, we obtain a weak Zhong-type variational principle in b-metric spaces. We show the applicability of the mentioned generalized variational principle by presenting a Caristi-type fixed point theorem and an extension of the main result for bifunctions - both of them stated in b-metric spaces.