Fixed Point Results for Two Mappings on Closed Balls in Continuous Controlled Metric Spaces with Applications to Urysohn Integral Equations
International Journal of Analysis and Applications, vol.24, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 24
- Publication Date: 2026
- Doi Number: 10.28924/2291-8639-24-2026-279
- Journal Name: International Journal of Analysis and Applications
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Keywords: closed ball, continuous controlled metric space, fixed point, Geraghty contraction, Geraghty-Ćirić contraction, Urysohn integral equation
- Open Archive Collection: AVESIS Open Access Collection
- Istanbul Gelisim University Affiliated: Yes
Abstract
This manuscript investigates complete continuous controlled metric spaces (CCMSs). New fixed point theorems are established under Geraghty and Geraghty-Ćirić type contractive conditions, formulated on a closed ball of a CCMS rather than on the entire space. This localized approach extends the existing fixed point theory in controlled metric spaces, where such results on closed balls have not been previously reported. Concrete examples are provided to illustrate the effectiveness of the obtained theorems. Furthermore, the applicability of the theoretical results is demonstrated by proving the existence and uniqueness of solutions for a system of Urysohn-type integral equations.