Simulation Functions and Fixed-Point Theorems in Orthogonal Bi-b-Metric Spaces with Applications to Volterra Integral Equations
DOI:
https://doi.org/10.46610/JOSME.2026.v12i03.005Keywords:
Common fixed point, Implicit relation, Nonlinear algebraic system, Orthogonal bi-b-metric space, Simulation function, Volterra integral equationsAbstract
Fixed point methods provide a useful framework for studying existence and uniqueness problems in nonlinear analysis. This work presents the development of common fixed-point results for two self-mappings defined on orthogonal bi-b-metric spaces. The proposed framework combines an orthogonality relation, a pair of b-metric structures, a simulation function, and an implicit contractive relation. Under suitable completeness, continuity, and preservation assumptions, the study establishes the existence and uniqueness of a common fixed point. The proof is constructed through an orthogonal iterative sequence and a Cauchy-type argument adapted to the bi-b-metric setting. A numerical example is included to illustrate the assumptions of the main theorem and to demonstrate how the simulation-function condition can be verified. As an application, the fixed point result is used to study a system of nonlinear Volterra integral equations. The associated operators are formulated on an appropriate space of continuous functions, and the hypotheses of the fixed point theorem are used to obtain existence and uniqueness of a solution. The proposed formulation brings together orthogonality, dual b-metric structure, and simulation functions in a single framework and provides a basis for further work on generalized metric spaces and nonlinear integral or fractional equations.
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