Turkish Journal of Mathematics
Author ORCID Identifier
YASEMİN BAŞCI: 0000-0003-3151-6467
ADİL MISIR: 0000-0002-4552-0769
SÜLEYMAN ÖĞREKÇİ: 0000-0003-1205-6848
Abstract
In this study, we investigate the existence of solutions for a quadratic integral equation of the Fredholm type. The analysis is conducted on a finite interval bounded by two arbitrary constants, where the unknown function is associated with a prescribed kernel and two operators satisfying specific regularity and boundedness conditions. The methodological framework of this work is built upon the classical Schauder fixed point theorem, complemented by the structural properties of Hölder spaces. The results obtained not only encompass but also extend several previous contributions in the literature, as the discussion is carried out within a generalized setting over the entire interval. Moreover, an illustrative example is provided to highlight the effectiveness and applicability of the proposed approach.
DOI
10.55730/1300-0098.3651
Keywords
Fredholm integral equation, Hölder space, Schauder fixed point theorem
First Page
281
Last Page
300
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
BAŞCI, Y, MISIR, A, & ÖĞREKÇİ, S (2026). On Fredholm type integral equations in H\"{o}der spaces: Existence of solutions. Turkish Journal of Mathematics 50 (2): 281-300. https://doi.org/10.55730/1300-0098.3651
