DOI: 10.24193/fpt-ro.2026.2.05

Authors: Huaping Huang, Mohamed Jleli, Bessem Samet

Abstract: In this paper we introduce two classes of single-valued mappings defined on metric spaces satisfying contractions involving the perimeters of ellipses. For each class, we obtain some suitable conditions under which the mapping possesses one and only one fixed point. Our exciting results include the famous Banach’s fixed point theorem as a special case. We also provide an interesting example in which our approach can be used while the Banach fixed point theorem is inapplicable. Moreover, we pose some open questions for further investigations. These questions point out the directions for studying fixed point theory and its applications in the upcoming future.

Key Words and Phrases: Fixed point, elliptic integral, elliptic contraction, complete metric space, polynomial type function

2020 Mathematics Subject Classification: 47H10, 54E40, 33E05.

Published on-line: June 1st, 2026.

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