IJPAM: Volume 102, No. 1 (2015)

ON FIXED POINT THEOREMS FOR
$(\xi$,$\alpha$,$\eta$)-EXPANSIVE MAPPINGS IN
COMPLETE METRIC SPACES

Ali Farajzadeh$^1$, Anchalee Kaewcharoen$^2$, Panisa Lohawech$^3$
$^{1}$Department of Mathematics
Razi University
Kermanshah, 67149, IRAN
$^{2,3}$Department of Mathematics
Faculty of Science
Naresuan University
Phitsanulok 65000, THAILAND


Abstract. In this paper, a new class of $(\xi, \alpha, \eta)$-expansive mappings is introduced which contains the class of generalized $(\xi, \alpha)$-expansive mappings has been posed by Karapinar et al. [Generalized ($\xi$,$\alpha$)-expansive mappings and related fixed-point theorems, Journal of Inequalities and Applications 2014, 2014:22]. Moreover, a representation for a generalized ($\xi$,$\alpha$)-expansive mapping is established and by applying it some conditions given in the literature by many authors in order to guarantee the existence of a fixed point are relaxed and by using some suitable conditions the existence of fixed points, in the setting of complete metric spaces as well as ordered complete metric spaces, for the new class of $(\xi, \alpha, \eta)$-expansive mappings is investigated. Furthermore, the relationship between having a fixed point for a map and being one-to-one of the map is discussed.

The results of this note can be viewed as an extension of the corresponding results have been presented in [3, 5, 7, 10, 11].

Received: April 8, 2015

AMS Subject Classification: 47H10, 54H25

Key Words and Phrases: $(\xi$,$\alpha$,$\eta$)-expansive mappings, fixed points, upper semicontinuity from the right

Download paper from here.



DOI: 10.12732/ijpam.v102i1.13 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 102
Issue: 1
Pages: 129 -


$(\xi$,$\alpha$,$\eta$)-EXPANSIVE MAPPINGS IN COMPLETE METRIC SPACES%22&as_occt=any&as_epq=&as_oq=&as_eq=&as_publication=&as_ylo=&as_yhi=&as_sdtAAP=1&as_sdtp=1" title="Click to search Google Scholar for this entry" rel="nofollow">Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).