Polynomial Reich Contractions of the Derivative Type in Metric Spaces with Applications
Abstract
Olatinwo [4] introduced contractions of the derivative type, and used them to prove a variant of the Banach fixed point theorem and theorems for implicit contractions. In this paper, some results concerning Reich polynomial contractions of the derivative type are established in metric spaces, together with an illustrative example. Finally, we apply our result to the Fredholm integral equation.
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References
Banach, S. (1922). Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fundamenta Mathematicae, 3(1), 133-181.
Jleli, M., Pacurar, C. M., & Samet, B. (2025). Fixed point results for contractions of polynomial type. Demonstratio Mathematica, 58(1), Article 20250098. https://doi.org/10.1515/dema-2025-0098
Reich, S. (1972). Fixed points of contractive functions. Bollettino dell'Unione Matematica Italiana, 6, 26-42.
Olatinwo, M. O. (2009). Some fixed point theorems involving weak contraction conditions of the derivative type. Octogon Mathematical Magazine, 17(2), 495-501.
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