Approximate fixed point theorems for Geraghty-contractions

Subject Areas : Applied Mathematics

ُS. A. M Mohsenalhoseini ¹ , H Mazaheri ²

1 - Valie-Asr University
2 - Islamic Azad University of Yazd

Received: 2015-04-22 Accepted : 2016-06-25 Published : 2016-12-01

Keywords:

Abstract :

The purpose of this paper is to obtain necessary and suffcient conditionsfor existence approximate fixed point on Geraghty-contraction. In this paper,denitions of approximate -pair fixed point for two maps Tα , Sα and theirdiameters are given in a metric space.

References:

[1] M. Berinde, Approximate Fixed Point Theorems,"Mathematica, vol. LI,
no. 1, 2006.
[2] M. Geraghty, On contractive mappings," Proc. Amer. Math. Soc. 40
(1973) 604-608.
[3] Jingling Zhang, Yongfu Su, Qingqing Cheng, Best proximity point
theorems for generalized contractions in partially ordered metric spaces,"
Fixed Point Theory and Applications 2013, 2013-200.

[4] J. Caballero et al., A best proximity point theorem for Geraghty-
contractions, Fixed Point Theory and Applications 2012, 2012-231.
[5] S.A.M. Mohsenalhosseini, H. Mazaheri, Fixed Point For completely norm
Space and map T, Mathematica Moravica. Vol. 16-2 (2012), 25-35.
[6] S. A. M. Mohsenalhosseini, H. Mazaheri, M. A. Dehghan, Approximate Best
Proximity Pairs in Metric Space, Abstract and Applied Analysis, Volume
2011, Article ID 596971, 9 pages.