Mathematics and Computational Sciences

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

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
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Mathematics and Computational Sciences
Volume 7, Issue 2
Spring 2026
Pages 72-87

  • Receive Date 29 January 2026
  • Revise Date 22 February 2026
  • Accept Date 20 April 2026

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