Fixed point theorems on generalized metric spaces for mappings in a class of almost \(\varphi\)-contractions
type: Item
instance of: scholarly article
title: Fixed point theorems on generalized metric spaces for mappings in a class of almost \(\varphi\)-contractions
zbMATH Open document ID: 1343.54014
author: Luljeta Kikina
author: Kristaq Kikina
published in: Demonstratio Mathematica
publication date: 2015-08-31T00:00:00Z
review text: In this paper, the authors obtained some sufficient conditions for the existence and uniqueness of fixed point for a contraction mapping satisfying an implicit relation in the framework of generalized metric space in the sense of \textit{A. Branciari} [Publ. Math. 57, No. 1--2, 31--37 (2000; Zbl 0963.54031)]. The results obtained generalize and extend the corresponding results of \textit{V. Berinde} [Nonlinear Anal. Forum 9, No. 1, 43--53 (2004; Zbl 1078.47042)], \textit{R. M. Tiberio Bianchini} [Boll. Unione Mat. Ital., IV. Ser. 5, 103--108 (1972; Zbl 0249.54023)], \textit{R. Kannan} [Am. Math. Mon. 76, 405--408 (1969; Zbl 0179.28203)] and of \textit{S. Reich} [Can. Math. Bull. 14, 121--124 (1971; Zbl 0211.26002)].
reviewed by: Sumit Chandok
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 6476933
zbMATH Keywords: Cauchy sequence
zbMATH Keywords: generalized metric spaces
zbMATH Keywords: fixed point
zbMATH Keywords: implicit relation
MaRDI profile type: Publication
full work available at URL: dema-2015-0031
OpenAlex ID: W2336278269
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DOI: 10.1515/DEMA-2015-0031
description: scientific article; zbMATH DE number 6476933