Fixed-Point Theorems for ℒγ Contractions in Branciari Distance Spaces

Cho, Seong‐Hoon

doi:10.3390/axioms11090479

Cited by 2 publications

(1 citation statement)

References 29 publications

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“…In 2018 and 2022, S. H. Cho [25,26] identified the specification of simulation functions, as stated beneath.…”

Section: Definition 4 ([16]) a Functionmentioning

confidence: 99%

On Modified Interpolative Almost E−Type Contraction in Partial Modular b−Metric Spaces

Kesik,

Büyükkaya,

Öztürk

2023

Axioms

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The current study attempts to identify a new generalized metric space structure, referred to as partial modular b−metric, that extends both partial modular metric space via b−metric space and explains the topological aspects of the new space implementing examples. In addition, a new contraction mapping referred to as modified interpolative almost E−type contraction is determined, which is an interpretation of interpolative contraction bestowed with almost contraction and E−contraction as well as a simulation function and a fixed point theorem that encompass such mappings in the context of partial modular b−metric space is demonstrated. In conclusion, an example and an application that endorse the main theorem’s outcomes are offered.

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“…In 2018 and 2022, S. H. Cho [25,26] identified the specification of simulation functions, as stated beneath.…”

Section: Definition 4 ([16]) a Functionmentioning

confidence: 99%

On Modified Interpolative Almost E−Type Contraction in Partial Modular b−Metric Spaces

Kesik,

Büyükkaya,

Öztürk

2023

Axioms

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On the Impact of Some Fixed Point Theorems on Dynamic Programming and RLC Circuit Models in R-Modular b-Metric-like Spaces

Girgin,

Büyükkaya,

Kuru

et al. 2024

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In this study, we significantly extend the concept of modular metric-like spaces to introduce the notion of b-metric-like spaces. Furthermore, by incorporating a binary relation R, we develop the framework of R-modular b-metric-like spaces. We establish a groundbreaking fixed point theorem for certain extensions of Geraghty-type contraction mappings, incorporating both Z simulation function and E-type contraction within this innovative structure. Moreover, we present several novel outcomes that stem from our newly defined notations. Afterwards, we introduce an unprecedented concept, the graphical modular b-metric-like space, which is derived from the binary relation R. Finally, we examine the existence of solutions for a class of functional equations that are pivotal in dynamic programming and in solving initial value problems related to the electric current in an RLC parallel circuit.

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Fixed-Point Theorems for ℒγ Contractions in Branciari Distance Spaces

Abstract: In this paper, the concepts of Suzuki-type \({\mathcal{L}_{\gamma}}\) contractions and Suzuki–Berinde-type \({\mathcal{L}_{\gamma}}\) contractions are introduced, and new fixed-point theorems for these two contractions are established.

Cited by 2 publications

References 29 publications

On Modified Interpolative Almost E−Type Contraction in Partial Modular b−Metric Spaces

On Modified Interpolative Almost E−Type Contraction in Partial Modular b−Metric Spaces

On the Impact of Some Fixed Point Theorems on Dynamic Programming and RLC Circuit Models in R-Modular b-Metric-like Spaces

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