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
Fixed Point Theory and Applications 2013, 2013:223 doi:10.1186/1687-1812-2013-223Published: 22 August 2013
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 -chainable PM-spaces and for cyclic operators.
MSC: 47H10, 54H25.