Displaying similar documents to “On Caristi's fixed point theorem in F-type topological spaces.”

Coincidence point theorems in certain topological spaces

Jong Soo Jung, Yeol Je Cho, Shin Min Kang, Yong Kab Choi, Byung Soo Lee (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

In this paper, we establish some new versions of coincidence point theorems for single-valued and multi-valued mappings in F-type topological space. As applications, we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.

Partial Fuzzy Metric Space and Some Fixed Point Results

Shaban Sedghi, Nabi Shobkolaei, Ishak Altun (2015)

Communications in Mathematics

Similarity:

In this paper, we introduce the concept of partial fuzzy metric on a nonempty set X and give the topological structure and some properties of partial fuzzy metric space. Then some fixed point results are provided.

On generalizations of fuzzy metric spaces

Yi Shi, Wei Yao (2023)

Kybernetika

Similarity:

The aim of the paper is to present three-variable generalizations of fuzzy metric spaces in sense of George and Veeramani from functional and topological points of view, respectively. From the viewpoint of functional generalization, we introduce a notion of generalized fuzzy 2-metric spaces, study their topological properties, and point out that it is also a common generalization of both tripled fuzzy metric spaces proposed by Tian et al. and ℳ -fuzzy metric spaces proposed by Sedghi...

On the generalizations of Siegel's fixed point theorem.

J. S. Jung, S. S. Chang, B. S. Lee, Y. J. Cho, S. M. Kang (2001)

Mathware and Soft Computing

Similarity:

In this paper, we establish a new version of Siegel's fixed point theorem in generating spaces of quasi-metric family. As consequences, we obtain general versions of the Downing-Kirk's fixed point and Caristi's fixed point theorem in the same spaces. Some applications of these results to fuzzy metric spaces and probabilistic metric spaces are presented.

On best approximation in fuzzy metric spaces

Naser Abbasi, Hamid Mottaghi Golshan (2015)

Kybernetika

Similarity:

In this paper we introduce the notation of t-best approximatively compact sets, t-best approximation points, t-proximinal sets, t-boundedly compact sets and t-best proximity pair in fuzzy metric spaces. The results derived in this paper are more general than the corresponding results of metric spaces, fuzzy metric spaces, fuzzy normed spaces and probabilistic metric spaces.

Caristi's fixed point theorem and its equivalences in fuzzy metric spaces

Naser Abbasi, Hamid Mottaghi Golshan (2016)

Kybernetika

Similarity:

In this article, we extend Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem to fuzzy metric spaces in the sense of George and Veeramani [A. George , P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems. 64 (1994) 395-399]. Further, a direct simple proof of the equivalences among these theorems is provided.