Year: 2026
Type: article
Abstract: This paper investigates fixed point results in convex double-controlled metric-type spaces. By introducing a convex structure on double-controlled metric-type spaces, we study the convergence of the Mann iteration process for contractive mappings in this framework. Under suitable conditions on the control functions, we establish the existence and uniqueness of fixed points and prove that the Mann iterative sequence converges to the fixed point. In addition, we investigate the stability of the Mann iteration process and establish a data dependence result. Finally, an application to a Fredholm integral equation is presented to illustrate the applicability of the obtained results.
Source: Mathematics
DOI: 10.3390/math14101620
Author: Nazli Kadioglu Karaca
Institution: Atatürk University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7160828969
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