Fixed Points and Mappings

Vidyadhar V. Nalawade; U. P. Dolhare

doi:https://doi.org/10.14445/22315373/IJMTT-V52P547

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 52 | Number 5 | Year 2017 | Article Id. IJMTT-V52P547 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P547

Fixed Points and Mappings

Vidyadhar V. Nalawade, U. P. Dolhare

Abstract

In this paper we give some important types of mappings related to the fixed point concept. We begin with the basic definition of mappings. Then we define self maps and commutative maps. We discuss about the existence of the fixed points of such mappings with examples. The main part of this research article deals mainly with the common fixed points of a class of polynomial functions. The polynomials considered here are self compositions of a given polynomial of degree n. We prove that if a polynomial and its first composition with itself have an identical set of fixed points, then the polynomial and its n th composition with itself also have an identical set of fixed points. Examples are provided to demonstrate the results. While considering the fixed point results in this article, we have not considered the metric space settings. All the fixed point theorems cited and proved in this paper are free from the distance concept.

Keywords

Mappings, Self Mappings, Commuting Mappings, Common Fixed Points.

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Citation :

Vidyadhar V. Nalawade, U. P. Dolhare, "Fixed Points and Mappings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 5, pp. 322-329, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P547