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

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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.

Topological degree theory in fuzzy metric spaces

M.H.M. Rashid (2019)

Archivum Mathematicum

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The aim of this paper is to modify the theory to fuzzy metric spaces, a natural extension of probabilistic ones. More precisely, the modification concerns fuzzily normed linear spaces, and, after defining a fuzzy concept of completeness, fuzzy Banach spaces. After discussing some properties of mappings with compact images, we define the (Leray-Schauder) degree by a sort of colimit extension of (already assumed) finite dimensional ones. Then, several properties of thus defined concept...

Partial Fuzzy Metric Space and Some Fixed Point Results

Shaban Sedghi, Nabi Shobkolaei, Ishak Altun (2015)

Communications in Mathematics

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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.

A new approach for KM-fuzzy partial metric spaces

Yu Shen, Chong Shen, Conghua Yan (2022)

Kybernetika

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The main purpose of this paper is to give a new approach for partial metric spaces. We first provide the new concept of KM-fuzzy partial metric, as an extension of both the partial metric and KM-fuzzy metric. Then its relationship with the KM-fuzzy quasi-metric is established. In particularly, we construct a KM-fuzzy quasi-metric from a KM-fuzzy partial metric. Finally, after defining the notion of partial pseudo-metric systems, a one-to-one correspondence between partial pseudo-metric...

On generalizations of fuzzy metric spaces

Yi Shi, Wei Yao (2023)

Kybernetika

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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

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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.

A new approach for fuzzy gyronorms on gyrogroups and its fuzzy topologies

Yu Shen, Conghua Yan (2024)

Kybernetika

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In this paper, a new approach for fuzzy gyronorms on gyrogroups is presented. The relations between fuzzy metrics(in the sense of Morsi), fuzzy gyronorms, gyronorms on gyrogroups are studied. Also, some sufficient conditions, which can make a fuzzy normed gyrogroup to be a topological gyrogroup and a fuzzy topological gyrogroup, are found. Meanwhile, the relations between topological gyrogroups, fuzzy topological gyrogroups and stratified fuzzy topological gyrogroups are studied. Finally,...

On best approximation in fuzzy metric spaces

Naser Abbasi, Hamid Mottaghi Golshan (2015)

Kybernetika

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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.