(αη)-contractive and (βχ)-contractive mapping based fixed point theorems in fuzzy bipolar metric spaces and application to nonlinear Volterra integral equations

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-08-23 DOI:10.1016/j.cnsns.2024.108307

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引用次数: 0

Abstract

In this paper, we introduce some novel concepts within the realm of fuzzy bipolar metric spaces, namely ( $α η$ )-contractive type covariant mappings and contravariant mappings, and ( $β χ$ )-contractive type covariant mappings. We establish some fixed point theorems that demonstrate both the existence and uniqueness of fixed points for ( $α η$ )-contractive type covariant mappings and contravariant mappings, and for ( $β χ$ )-contractive type covariant mappings in complete fuzzy bipolar metric spaces utilizing the triangular property. Additionally, to substantiate the findings, some illustrative examples and consequential outcomes are presented. Furthermore, the proven results serve to extend, generalize, and enhance the corresponding outcomes documented in existing literature. A practical application of these findings in the context of non-linear Volterra integral equations is demonstrated, solidifying and reinforcing the credibility of the established results. Overall, this paper contributes to the understanding of fixed point theory in the context of fuzzy bipolar metric spaces and highlights the significance of ( $α η$ )-contractive mappings and ( $β χ$ )-contractive mappings in this domain.

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模糊双极度量空间中基于 (αη)-contractive 和 (βχ)-contractive 映射的定点定理及其在非线性 Volterra 积分方程中的应用

本文介绍了模糊双极度量空间领域的一些新概念，即(αη)-收缩型协变映射和逆变映射，以及(βχ)-收缩型协变映射。我们建立了一些定点定理，利用三角形性质证明了完整模糊双极度量空间中的（αη）-收缩型协变映射和协变映射，以及（βχ）-收缩型协变映射的定点的存在性和唯一性。此外，为了证实这些发现，还提出了一些示例和相应的结果。此外，这些已证实的结果有助于扩展、概括和加强现有文献中记载的相应成果。本文展示了这些发现在非线性 Volterra 积分方程中的实际应用，巩固并加强了既定结果的可信度。总之，本文有助于理解模糊双极度量空间背景下的定点理论，并强调了 (αη)-contractive 映射和 (βχ)-contractive 映射在这一领域的重要意义。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.