Cholatis Suanoom, Natthaphon Artsawang, Anteneh Getachew Gebrie, Fixed point and convergence theorems in convex $(\theta_1, \theta_2)$-extended b-metric spaces with applications to integral equations, Vol. 2025 (2025), No. 36, pp. 1-12

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DOI: 10.23952/jnfa.2025.36

Received May 25, 2025; Accepted September 26, 2025; Published November 5, 2025

Abstract.This paper introduces a novel mathematical framework known as the convex $(\theta_1,\theta_2)$ -extended $b$ -metric space, which generalizes the classical metric and $b$ -metric settings. Within this structure, we establish fixed-point theorems and convergence results by employing both contraction-type and interpolative techniques. In particular, we develop enriched fixed-point results, extend Mann’s iterative algorithm, and investigate fixed points of $\omega$ -operators under generalized contractive conditions. The theoretical findings are further supported by applications to nonlinear integral equations of Volterra type. We demonstrate the effectiveness of the proposed theorems in proving existence and uniqueness of solutions within the generalized space. Moreover, numerical examples are provided to illustrate the convergence behavior of iterative sequences, highlighting the practical relevance and applicability of the main results.

How to Cite this Article:
C. Suanoom, N. Artsawang, A.G. Gebrie, Fixed point and convergence theorems in convex $(\theta_1, \theta_2)$ -extended $b$ -metric spaces with applications to integral equations, J. Nonlinear Funct. Anal. 2025 (2025) 36.