المجلة العالمية للعلوم التطبيقية

ABSTRACT
Fixed point theory in generalized metric spaces has emerged as an important framework for addressing nonlinear problems and differential equations beyond the classical metric setting. In this study, we develop a unified fixed point framework in (M^*)-metric spaces, extending and generalizing several existing approaches in (M_b)-metric, (M_R)-metric, and (\Omega_b)-distance spaces. The proposed framework is motivated by the need for more flexible generalized distance structures capable of accommodating complex nonlinear problems, particularly those arising in fractional calculus and differential equations.
The principal contribution of this work is the establishment of new fixed point results for mappings defined on complete (M^)-metric spaces. In particular, we prove a common fixed point theorem for two mappings (S,T\rightarrow X) satisfying a generalized contractive condition of the form[M^(S\zeta,T\kappa,T\kappa)\leq \lambda M^(\zeta,\kappa,\kappa),\qquad \lambda\in[0,1),]
and demonstrate the existence and uniqueness of a common fixed point. The proof is developed through the construction of interwoven iterative sequences, contraction estimates, the Cauchy property, and completeness of the underlying (M^)-metric space. The results further extend existing contraction principles and establish connections with weak contraction, simulation function, admissibility, and interpolative contraction approaches.
To illustrate the applicability of the theoretical findings, a detailed example is provided in a complete (M^)-metric space, demonstrating the convergence behavior of the constructed sequences toward the common fixed point. Beyond the theoretical developments, the proposed results provide a foundation for applications to nonlinear operators and fractional differential equations, while offering potential computational approaches related to atomic solution methods. Overall, this study strengthens the theoretical framework of generalized fixed point theory by providing new common fixed point results in (M^)-metric spaces and broadening their potential applications in nonlinear analysis, fractional calculus, and computational mathematics.

Keywords: M∗-metric spaces; Fixed point theory; Nonlinear contractions; Fractional calculus; Simulation functions

المراجع

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Article history

Received : Apr 22, 2025

Revised : Apr 27, 2025

Accepted : Aug 11, 2025

Authors Affiliations

Mohd Qasim Surmat a,1,*,

a Department of Mathematics Education, Universitas Islam Negeri Syarif Hidayatullah Jakarta, Indonesia, Email: surmat.Mohd@uinjkt.ac.id

* Corresponding Author Mohd Qasim Surmat, surmat.Mohd@uinjkt.ac.id

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