Open Access Research

Probabilistic G-contractions

Tayyab Kamran1, Maria Samreen2 and Naseer Shahzad3*

Author Affiliations

1 Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

2 Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, H-12, Islamabad, Pakistan

3 Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

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Fixed Point Theory and Applications 2013, 2013:223  doi:10.1186/1687-1812-2013-223

Published: 22 August 2013

Abstract

In this paper we introduce the notion of probabilistic G-contraction and establish some fixed point theorems in such settings. Our results generalize/extend some recent results of Jachymski and Sehgal and Bharucha-Reid. Consequently, we obtain fixed point results for <a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2013/1/223/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2013/1/223/mathml/M1">View MathML</a>-chainable PM-spaces and for cyclic operators.

MSC: 47H10, 54H25.

Keywords:
fixed point; Menger PM-space; directed graph; Picard operator