DOI: 10.24193/fpt-ro.2022.2.16

Authors: Ioan A. Rus

Abstract: In the book, Fixed Point Structure Theory (I.A. Rus, Fixed Point Structure Theory, Cluj Univ. Press, Cluj-Napoca, 2006) there are studied fixed point structures on a set with structure. In this paper we introduce the notion of the set-mapping pair (𝒰, M) (i.e., 𝒰 := a class of sets with the same type structure and for X, Y ∈ 𝒰 a set of mappings, M(X, Y), from X to Y is given) and the notion of fixed point structure (f.p.s.) on a such pair. After some examples of f.p.s. we study the preserving of the fixed point property by, (𝒰, M)-bijections, retractions, cartesian product and exponential. We give some fixed point results in terms of a f.p.s. and we consider some special f.p.s.: f.p.s. with common fixed point property, with coincidence point property and with coincidence producing mappings. Some open problems are also formulated.

Key Words and Phrases: Set with structure, set-mapping pair, category of sets with structure, fixed point structure, retraction, coretraction, coincidence point property, common fixed point property, coincidence producing mapping, cartesian product, exponential.

2010 Mathematics Subject Classification: 47H10, 54H25, 06xx, 18Axx, 54Cxx, 55M20, 58J20, 03xx, 68xx.

Published on-line: June 15th, 2022.

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