1,230 research outputs found
New generalized fuzzy metrics and fixed point theorem in fuzzy metric space
In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature
Contractive maps in locally transitive relational metric spaces
Some fixed point results are given for a class of Meir-Keeler contractive
maps acting on metric spaces endowed with locally transitive relations.
Technical connections with the related statements due to Berzig et al [Abstr.
Appl. Anal., Volume 2013, Article ID 259768] are also being discussed.Comment: arXiv admin note: text overlap with arXiv:1211.417
A new proof of the Lie-Trotter-Kato formula in Hadamard spaces
The Lie-Trotter-Kato product formula has been recently extended into Hadamard
spaces by [Stojkovic, Adv. Calc. Var., 2012]. The aim of our short note is to
give a simpler proof relying upon weak convergence instead of an ultrapower
technique.Comment: arXiv admin note: text overlap with arXiv:1211.041
Multivalued generalizations of fixed point results in fuzzy metric spaces
This paper attempts to prove fixed and coincidence point results in fuzzy metric space using multivalued mappings. Altering distance function and multivalued strong {bn}-fuzzy contraction are used in order to do that. Presented theorems are generalization of some well known single valued results. Two examples are given to support the theoretical results
Symmetric Spaces and Fixed Points of Generalized Contractions
Some fixed point results in semi-metric spaces as well as in symmetric spaces are proved. Applications of our results to probabilistic spaces are also presented
Unified multi-tupled fixed point theorems involving mixed monotone property in ordered metric spaces
In the present article, we introduce a unified notion of multi-tupled fixed
points and utilize the same to prove some existence and uniqueness unified
multi-tupled fixed point theorems for Boyd-Wong type nonlinear contractions
satisfying generalized mixed monotone property in ordered metric spaces. Our
results unify several classical and well-known n-tupled (including coupled,
tripled and quadrupled ones) fixed point results existing in the literature.Comment: arXiv admin note: substantial text overlap with arXiv: 1601.0251
Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces
Very recently, Proinov introduced a great family of contractions in the setting of complete
metric spaces that has attracted the attention of many researchers because of the very weak conditions
that are assumed on the involved functions. Inspired by Proinov’s results, in this paper, we introduce
a new class of contractions in the setting of fuzzy metric spaces (in the sense of George and Veeramani)
that are able to translate to this framework the best advantages of the abovementioned auxiliary
functions. Accordingly, we present some results about the existence and uniqueness of fixed points
for this class of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces
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