Fixed point theory approach in vector-valued metric spaces for the solvability of multivariate integral equation systems

Amiri, Pari

doi:10.30511/mcs.2026.2084051.1716

Fixed point theory approach in vector-valued metric spaces for the solvability of multivariate integral equation systems

Articles in Press

Document Type : Original Article

Author

Pari Amiri

Department of Advanced Sciences, Faculty of Advanced Technologies, University of Mohaghegh Ardabili, Namin, Iran

https://doi.org/10.30511/mcs.2026.2084051.1716

Abstract

‎This study investigates the existence of solutions for certain systems of integral equations in multi-component models with asymmetric and ‎heterogeneous dynamics‎, ‎using fixed point theory‎. ‎Classical metric frameworks are not sufficiently flexible to adequately capture these systems‎, ‎highlighting the need for more flexible‎‏ ‎approaches‎. ‎To address these challenges‎, ‎a Perov-type vector-valued metric space endowed with a triangle inequality controlled by two matrices is introduced‎, ‎which extends classical metric‎ ‎frameworks by incorporating two independent control matrices‎. ‎
This double-controlled structure significantly enlarges the admissible class of mappings and allows component-wise control adapted to heterogeneous dynamics. Within this setting, the concept of $\mathbb{M}_\alpha$-admissible pairs of selfmaps is defined, and new common fixed point theorems under generalized matrix-type contraction conditions are established, extending several existing results in the literature. ‎The proposed methodology is applied to a two-dimensional integral equation system‎, ‎and a numerical example is presented to validate the theoretical results‎.‎‎

Keywords

&lrm

Common fixed point, $\mathbb{M}_\alpha-$admissible pair of selfmaps, Perov-type vector-valued metric spaces with double-controlled triangle inequality, &lrm

Integral equation systems

Subjects