Affiliation:
1. Babeş-Bolyai University of Cluj-Napoca , Department of Mathematics , 1 M. Kogălniceanu, 400084 Cluj-Napoca , Romania
Abstract
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.
Reference40 articles.
1. [1] H. Amann, Order structures and fixed points, SAFA 2, Univ. of Calabria, 1977, 1–51.
2. [2] C. Avramescu, Asupra unei teoreme de punct fix, St. Cerc. Mat. 22 (1970), No. 2, 215–221.
3. [3] M. Barr, C. Wells, Category Theory for Computing Science, Prentice Hall, New York, 1990.
4. [4] G. Beer, More on convergence of continuous functions and topological convergence of sets, Canad. Math. Bull. 28 (1985), 52–59.10.4153/CMB-1985-004-9
5. [5] V. Berinde, A. Petruşel, I.A. Rus and M.A. Şerban, The retraction-displacement condition in the theory of fixed point equation with a convergent iterative algorithm, in: T.M. Rassias and V. Gupta (Eds.), Mathematical Analysis, Approximation Theory and Their Applications, Springer, 2016, 75–106.10.1007/978-3-319-31281-1_4