Fixed point results for Suzuki‐type Σ‐contractions via simulation functions in modular <i>b</i>‐metric spaces

Öztürk, Mahpeyker; Büyükkaya, Abdurrahman

doi:10.1002/mma.7634

Cited by 6 publications

(1 citation statement)

References 29 publications

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“…where E (x , y) is defined as (14), for all distinct x , y ∈ M * ρ − Fix(Y ) and for all λ > 0. Thereupon, Y owns a unique fixed point.…”

Section: Corollary 3 Letmentioning

confidence: 99%

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

Kesik,

Büyükkaya,

Öztürk

2023

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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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“…where E (x , y) is defined as (14), for all distinct x , y ∈ M * ρ − Fix(Y ) and for all λ > 0. Thereupon, Y owns a unique fixed point.…”

Section: Corollary 3 Letmentioning

confidence: 99%

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

Kesik,

Büyükkaya,

Öztürk

2023

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On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces with an Application

BÜYÜKKAYA,

ÖZTÜRK

2024

Communications in Advanced Mathematical Sciences

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In this paper, by taking ${{\mathcal C}_\mathcal{A}}-$simulation function and Proinov type function into account, we set up a new contraction mapping, which is referred to as Suzuki$-$Proinov $\mathpzc{Z^*}_{\aE^*}^{\aR}(\alpha)-$contraction and including both rational expressions that have quadratic terms and $\aE-$type contraction. Furthermore, we demonstrate a common fixed point theorem through the mappings endowed with triangular $\alpha-$admissibility in the setting of modular $b-$metric space. Besides that, we achieve some new outcomes that contribute to the current ones in the literature through the main theorem, and, as an application, we examine the existence of solutions to a class of functional equations emerging in dynamic programming.

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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 results for Suzuki‐type Σ‐contractions via simulation functions in modular b‐metric spaces

Cited by 6 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 Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces with an Application

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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