Some fixed point theorems in regular modular metric spaces and application to Caratheodory’s type anti-periodic boundary value problem

Sanatee, Ali Ganjbakhsh; Rathour, Laxmi; Mishra, Vishnu Narayan; Dewangan, Vinita

doi:10.1007/s41478-022-00469-z

Cited by 8 publications

(3 citation statements)

References 17 publications

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“…In their research published in [16], Omran et al made a significant discovery by establishing Banach fixed-point theorems within the context of generalized metric spaces equipped with the Hadamard product, offering fresh perspectives on this fundamental concept. It is worth noting that a plethora of other noteworthy results related to fixed point theory and its myriad of applications can be found in references [17][18][19][20][21][22][23][24][25], collectively contributing to the ever-evolving landscape of fixed-point theory and its multifaceted implications.…”

Section: Introductionmentioning

confidence: 99%

A Quicker Iteration Method for Approximating the Fixed Point of Generalized α-Reich-Suzuki Nonexpansive Mappings with Applications

Ali,

Pompei-Cosmin

et al. 2023

Fractal Fract

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Fixed point theory is a branch of mathematics that studies solutions that remain unchanged under a given transformation or operator, and it has numerous applications in fields such as mathematics, economics, computer science, engineering, and physics. In the present article, we offer a quicker iteration technique, the D** iteration technique, for approximating fixed points in generalized α-nonexpansive mappings and nearly contracted mappings. In uniformly convex Banach spaces, we develop weak and strong convergence results for the D** iteration approach to the fixed points of generalized α-nonexpansive mappings. In order to demonstrate the effectiveness of our recommended iteration strategy, we provide comprehensive analytical, numerical, and graphical explanations. Here, we also demonstrate the stability consequences of the new iteration technique. We approximately solve a fractional Volterra–Fredholm integro-differential problem as an application of our major findings. Our findings amend and expand upon some previously published results.

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Section: Introductionmentioning

confidence: 99%

A Quicker Iteration Method for Approximating the Fixed Point of Generalized α-Reich-Suzuki Nonexpansive Mappings with Applications

Ali,

Pompei-Cosmin

et al. 2023

Fractal Fract

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“…Particularly, if for all , thus, a lipschitzian type semigroup reduces to an asymptotically nonexpansive type semigroup. It is easy to see that the class of lipschitzian type semigroups contains the class of lipschitzian semigroups [6]- [8].…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Theorems for Semigroups of Lipschitzian Mappings

Marom,

Istiqlal

2023

J. Multidiscip. Appl. Nat. Sci.

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“…Since the Banach Contraction Principle, many scholars have developed it by changing the contraction environment and changing the metric type, e.g., [1][2][3][4][5][6][7][8][9][10][11]. For instance, in 2004, Ran and Reurings [1] introduced partial order in metric spaces and proposed some fixed point results in such spaces.…”

Section: Introductionmentioning

confidence: 99%

Coupled Fixed Point Theorems with Rational Type Contractive Condition via C-Class Functions and Inverse Ck-Class Functions

et al. 2022

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The purpose of this paper is to develop coupled fixed point theorems by C-class functions with mixed monotonicity, discuss the existence of the coupled fixed point of two mappings and obtain a coupled coincidence point theorem via inverse Ck-class functions in partially ordered H-metric spaces. This improves the existing results. In addition, some instances and an application are given to illustrate the usability and validity of the results.

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Some fixed point theorems in regular modular metric spaces and application to Caratheodory’s type anti-periodic boundary value problem

Cited by 8 publications

References 17 publications

A Quicker Iteration Method for Approximating the Fixed Point of Generalized α-Reich-Suzuki Nonexpansive Mappings with Applications

A Quicker Iteration Method for Approximating the Fixed Point of Generalized α-Reich-Suzuki Nonexpansive Mappings with Applications

Fixed Point Theorems for Semigroups of Lipschitzian Mappings

Coupled Fixed Point Theorems with Rational Type Contractive Condition via C-Class Functions and Inverse Ck-Class Functions

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