Fixed point structures on a set-mapping pair and cartesian product

Ioan A. Rus; Marcel-Adrian Şerban

doi:10.2478/awutm-2022-0012

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Fixed point structures on a set-mapping pair and cartesian product

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 58 (2022): Issue 2 (December 2022)

By: Ioan A. Rus and Marcel-Adrian Şerban

Open Access

|Dec 2022

Abstract

In this paper we study the following problem (Problem 4.2 in, I.A. Rus, Sets with structure, mappings and fixed point property: fixed point structures, Fixed Point Theory 23, No. 2 (2022), 689-706):

Let (𝒰, 𝒮, M) be a fixed point structure on (𝒰, M). We suppose that (𝒰, M) is with cartesian product. In which conditions, we have that:

X,Y∈𝒮⇒X×Y∈𝒮?

Some results in terms of exponential with fixed point property are also given. The basic results are illustrated by examples.

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Articles in this issue

DOI: https://doi.org/10.2478/awutm-2022-0012 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

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Language: English

Page range: 3 - 11

Published on: Dec 24, 2022

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

category of sets with structure,

set-mapping pair,

fixed point structure,

cartesian product,

fixed point selection property,

exponential with fixed point property,

cartesian product with fixed point property,

ordered set with fixed point property,

metric space with fixed point property,

topological space with fixed point property

Related subjects:

Mathematics,

General mathematics

© 2022 Ioan A. Rus, Marcel-Adrian Şerban, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 58 (2022): Issue 2 (December 2022)