DOI: 10.24193/fpt-ro.2023.1.14

Authors: Imed Kedim and Maher Berzig

Abstract: We establish a new fixed point theorem in abstract spaces. We then derive two main consequences in topological spaces for mappings admitting precompact images or leading to a nonempty ω-limit set. The study is carried out by introducing a cone of special functions which enables us to extend, unify and improve fixed point results due to Bailey, Ćirić, Dass-Gupta, Edelstein, Hardy-Rogers, Jaggi, Karapınar, Liepiņš, Nemytskii, Popa, Popescu, Reich, Suzuki and Wardowski. Finally, we introduce the notion of ξ-Lipschitz property and we investigate the existence of solutions to a class of Cauchy problems.

Key Words and Phrases: Fixed points, precompact, omega-limit sets, Cauchy problems.

2010 Mathematics Subject Classification: 47H10, 54Axx, 37C25, 34G20.

Published on-line: February 1st, 2023.

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