An abstract metric space and some fixed point theorems with an application to Markov process

In this paper we prove some generalized fixed point theorems for a class of contractive mappings over an extended JS-generalized metric space. Notions of weakly sensitive and strongly sensitive coefficient functions have been used here in proving fixed point theorems. Examples are given in strengthening the hypothesis of our established theorems. Moreover an application is given to fixed circle problem.

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“…Now we give the definition of a newly introduced space called extended JS-generalized metric space. Next we discuss about such spaces (See [16]).…”

Section: ] Be the Space Of All Real Functionsmentioning

confidence: 99%

“…Recently Roy and Saha have introduced the concept of extended JSgeneralized metric space [16] which includes the concepts of many of our known metric like spaces and have been able to prove some fixed point theorems therein.…”

Section: Introductionmentioning

confidence: 99%

Fixed point theorems for a class of extended JS contraction mappings over a generalized metric space with an application to fixed circle problema

Roy

Saha

2022

Proyecciones (Antofagasta)

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“…This outcome has been demonstrated to be an extremely helpful instrument for ensuring the existence and originality of answers to many types of difficult issues that arise in a variety of fields both inside and outside of mathematics. The traditional Banach contraction concept has been expanded upon and developed in a variety of ways (see [13,14,19,12,8,6,16,20]).…”

Section: Introductionmentioning

confidence: 99%

“…In order to broaden the scope of applicability, S. Czerwik [5] developed the idea of bMS as a notional advancement of metric spaces and demonstrated fixed point findings as a counterpart to the Banach contraction theorem. As a matter of fact, a sizeable body of work has already been written about the theory of fixed point in bMS for single valued and multivalued mappings (see [4,16,3,5,18,9]). Definition 1.2.…”

Section: Introductionmentioning

confidence: 99%

Solution of an algebraic linear system of equations using fixed point results in C∗−algebra valued extended Branciari Sb−metric spaces

Alam

Rohen

2023

Preprint

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Two new types of metric spaces namely C∗−algebra valued Branciari Sb−metric space and C∗−algebra valued extended Branciari Sb−metric space are introduced in this work, which are a generalization of all known related metric spaces.We explained the generalizations with two examples respectively. There are examples of self-mappings having a unique fixed point, which are concluded using our main theorems. As an application, we used one of our main results to show the existence of a unique solution of an algebraic system of linear equations with a numerical example. Mathematics Subject Classification (2010). Primary 54H25; Secondary 47H10.

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“…One of those is the concept of b-metric spaces which was introduced by Czerwik [6] in 1993. The concepts of metric and b-metric structures have been generalized in many ways (see [3,4,10,15,16,17,18,19,20,21,22,23]). Branciari [5] presented rectangular metric space in 2000, another such generalized metric structure, where the triangle inequality had been replaced by a so-called quadrilateral or rectangular inequality.…”

Section: Introductionmentioning

confidence: 99%

Controlled v-generalized metric type space and some fixed point theorems with application

Roy,

Saha,

Parvaneh

et al. 2023

Preprint

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In this article, the concept of controlled v-generalized metric type space is introduced as a generalization of b v (s)-metric spaces and controlled metric type spaces. Some fixed point theorems are proved for Banach orbital contractions and Bianchini type contractions over such spaces. Several examples are given in respect of our new metric type structure and established theorems. In addition, we use our fixed point theorems to find solutions to nonlinear integral equations. AMS subject classification (2020): 47H10; 54H25.

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An abstract metric space and some fixed point theorems with an application to Markov process

Cited by 7 publications

References 7 publications

Fixed point theorems for a class of extended JS contraction mappings over a generalized metric space with an application to fixed circle problema

Fixed point theorems for a class of extended JS contraction mappings over a generalized metric space with an application to fixed circle problema

Solution of an algebraic linear system of equations using fixed point results in C∗−algebra valued extended Branciari Sb−metric spaces

Controlled v-generalized metric type space and some fixed point theorems with application

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