Common fixed point theorems for contractive mappings satisfying Φ-maps in S-metric spaces

Sedghi, Shaban; Rezaee, Mohammad Mahdi; Došenović, Tatjana; Radenović, Stojan

doi:10.1515/ausm-2016-0020

Cited by 15 publications

(13 citation statements)

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“…Similarly, if Sðy 2nÀ1 ; y 2nÀ1 ; y 2nÀ2 Þ\Sðy 2n ; y 2n ; y 2nÀ1 Þ for some n 2 N then from (11), we obtain Sðy 2n ; y 2n ; y 2nÀ1 Þ ða 1 þ 3a 2 þ 3a 4 þ a 5 ÞSðy 2n ; y 2n ; y 2nÀ1 Þ \Sðy 2n ; y 2n ; y 2nÀ1 Þ;…”

Section: Common Fixed Point Resultsunclassified

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Common fixed point of four maps in S-metric spaces

et al. 2018

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In this paper, we prove some common fixed point results for four mappings satisfying generalized contractive condition in S-metric space. Our results extend and improve several previous works. Keywords Common fixed point Á S-metric space Á Compatible mappings Mathematics Subject Classification 47H10 Á 54H25 1. Sðx; y; zÞ ¼ 0 if and only if x ¼ y ¼ z; 2. Sðx; y; zÞ Sðx; x; aÞ þ Sðy; y; aÞ þ Sðz; z; aÞ:The pair (X, S) is called an S-metric space. Example 1.2 [1]We can easily check that the following examples are S-metric spaces.1. Let X ¼ R n and jj Á jj be a norm on X. Then Sðx; y; zÞ ¼ jjy þ z À 2xjj þ jjy À zjj is an S-metric on X. In general, if X is a vector space over R and jj Á jj is a norm on X. Then it is easy to see that Sðx; y; zÞ ¼ jjay þ bz À kxjj þ jjy À zjj;where a þ b ¼ k for every a; b ! 1, is an S-metric on X. 2. Let X be a nonempty set and d 1 , d 2 be two ordinary metrics on X. Then Sðx; y; zÞ ¼ d 1 ðx; zÞ þ d 2 ðy; zÞ;is an S-metric on X.Mathematical Sciences (2018) 12:137-143 https://doi.org/10.1007/s40096-018-0252-6( 0123456789().,-volV) (0123456789().,-volV)

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Section: Common Fixed Point Resultsunclassified

“…They introduced a notion of S-metric spaces and give some of their properties. For more details regarding this spaces we refer [1][2][3][4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Common fixed point of four maps in S-metric spaces

et al. 2018

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“…Due to great importance of the fixed point theory, it is immensely interesting to study fixed point theorems on different concepts. Many authors studied the fixed points for mappings satisfying contractive conditions in complete S-metric spaces (see, e.g., [6,11,13,14,20,23,25,26]) and others).…”

Section: Introductionmentioning

confidence: 99%

Fixed point theorems on cone S-metric spaces using implicit relation

Saluja

2020

Cubo

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In this paper, we establish some fixed point theorems in the framework of cone S-metric spaces using implicit relation. Our results extend, unify and generalize several results from the current existing literature. Especially, they extend the corresponding results of Sedghi and Dung [24] to the setting of complete cone S-metric spaces. RESUMEN En este artículo, establecemos algunos teoremas de punto fijo en el marco de espacios S-métricos del cono usando una relación implícita. Nuestros resultados extienden, unifican y generalizan diversos resultados de la literatura actual existente. Especialmente, extienden los resultados correspondientes de Sedghi y Dung [24] en el contexto de espacios S-métricos de cono completo.

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“…Taking T = S in the above theorem we get the following corollary unifying Vasuki's Theorem 1.9 [11], which in turn also generalizes the result of Pant [5]. Corollary 2.2: Let S be a continuous self mappings of a complete ℳ-fuzzy metric space (X, ℳ,*), where * is a continuous t-norm.…”

Section: Fixed Point Theorem For Three Self Mapsmentioning

confidence: 55%