Approximate fixed point theorems for Geraghty-contractions

Theory of Approximation and Applications

مقاله 3، دوره 10، شماره 2، اسفند 2016، صفحه 23-32   

نوع مقاله: Research Articles

نویسندگان

ُS. A. M Mohsenalhoseini^{* 1}؛ H Mazaheri²

¹Valie-Asr University

²Islamic Azad University of Yazd

چکیده

The purpose of this paper is to obtain necessary and suffcient conditions
for existence approximate fixed point on Geraghty-contraction. In this paper,
denitions of approximate -pair fixed point for two maps T_α , S_α and their
diameters are given in a metric space.

کلیدواژه‌ها

Approximate fixed point؛ Approximate-pair fixed point؛ Geraghty-contraction

مراجع

[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.