A power mapping and its fixed points

Authors

  • Seid Mohammad Anvariyeh Department of Mathematical Sciences-Yazd University-Yazd-Iran
  • Seid Morteza Musavi A. Department of Mathematical Sciences, Yazd University, Yazd, Iran

DOI:

https://doi.org/10.30495/jme.v18i0.3109

Keywords:

Set-valued mapping, Power mapping, Fixed point

Abstract

In this paper, we show that for a nonempty finite set $U$ and a power mapping $T:U\longrightarrow \mathcal{P}^*(U)$, there exists a nonempty subset $F$ of $U$ such that $T'(F) = F$ where $T'(F)=\bigcup_{x\in F}T(x)$.  Also for a power mapping $T:U \longrightarrow \mathcal{P}(U)$, we get an equivalent condition for having a nonempty fixed points set. Finally, we present a method to obtain all of fixed point of $T$.

Author Biographies

Seid Mohammad Anvariyeh, Department of Mathematical Sciences-Yazd University-Yazd-Iran

Associate Professor of Mathematics, Yazd University

Seid Morteza Musavi A., Department of Mathematical Sciences, Yazd University, Yazd, Iran

Doctoral student of Yazd University

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Published

2025-02-15

Issue

Vol. 18

Section

Vol. 18, No. 11, (2024)

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