A generalization of Matkowski’s and Suzuki’s fixed point theorems

Khantwal, Deepak; Aneja, Surbhi; Gairola, U. C.

doi:10.1142/s1793557122501698

Cited by 4 publications

(2 citation statements)

References 6 publications

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“…In 1922, Banach [1] introduced the theory of fixed points; this theory has been further developed through generalizations of linear and nonlinear contractions [2,3]. Generalizations have been made for metric spaces, such as the b metric space and its generalization [4], as well as the J metric space [5], and many more such as [6]. However, all of these extensions assume that the self-distance is zero.…”

Section: Introductionmentioning

confidence: 99%

A New Extension of CJ Metric Spaces—Partially Controlled J Metric Spaces

et al. 2023

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This article introduces the concept of partially controlled J metric spaces; in particular, the J metric space with self-distance is not necessarily zero, which is important in computer science. We prove the existence of a unique fixed point for linear and nonlinear contractions, provide some examples to prove the existence of this metric space, and present some important applications in fractional differential equations, i.e., “Riemann–Liouville derivatives”.

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Section: Introductionmentioning

confidence: 99%

A New Extension of CJ Metric Spaces—Partially Controlled J Metric Spaces

et al. 2023

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“…The Banach contraction principle (BCP) is a fundamental theorem in classical mathematics. Drawing upon this initial framework, other scholars have expanded and broadened the concept of the BCP to incorporate a wide range of circumstances and maps (see [1][2][3][4][5][6][7][8]).…”

Section: Introductionmentioning

confidence: 99%

The Stability and Well-Posedness of Fixed Points for Relation-Theoretic Multi-Valued Maps

Letlhage,

Khantwal,

Pant

et al. 2023

Mathematics

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The purpose of this study is to present fixed-point results for Suzuki-type multi-valued maps using relation theory. We examine a range of implications that arise from our primary discovery. Furthermore, we present two substantial cases that illustrate the importance of our main theorem. In addition, we examine the stability of fixed-point sets for multi-valued maps and the concept of well-posedness. We present an application to a specific functional equation which arises in dynamic programming.

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Some existence and uniqueness results for a solution of a system of equations

Khantwal,

Pant

2024

Appl. Gen. Topol.

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This paper presents some existence and uniqueness results for a system of mappings on the finite product of metric spaces. Our results extend and generalize the well-known and celebrated results of Boyd and Wong [Proc. Amer. Math. Soc. 20 (1969)], Matkowski [Dissertations Math. (Rozprawy Mat.) 127 (1975)], Proinov [Nonlinear Anal. 64 (2006)], Song-il Ri [Indag. Math. (N. S.) 27 (2016)] and many others. We also present some illustrative examples to validate our results.

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A generalization of Matkowski’s and Suzuki’s fixed point theorems

Abstract: In this paper, we present a generalization of Suzuki’s fixed point theorem and the Matkowski contraction principle for a system of transformations on the finite product of metric spaces.

Cited by 4 publications

References 6 publications

A New Extension of CJ Metric Spaces—Partially Controlled J Metric Spaces

A New Extension of CJ Metric Spaces—Partially Controlled J Metric Spaces

The Stability and Well-Posedness of Fixed Points for Relation-Theoretic Multi-Valued Maps

Some existence and uniqueness results for a solution of a system of equations

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