Common fixed point theorems of Meir-Keeler type in metric spaces


	Open access
	Common fixed point theorems of Meir-Keeler type in metric spaces


	Fixed Point Theory, Volume 18, No. 1, 2017, 17-26, March 1st, 2017 DOI: 10.24193/fpt-ro.2017.1.02 Authors: Mortaza Abtahi Abstract: This paper is a continuation of the recent work [M. Abtahi, Fixed point theorems for Meir-Keeler type contractions in metric spaces, Fixed Point Theory, 17(2016), No. 2, 225-236]. After establishing a criterion for sequences in metric spaces to be Cauchy, unified simple proofs for several known results on the existence of a common fixed point for compatible pairs of mappings of complete metric spaces satisfying a contractive condition of Meir-Keeler type are obtained. A very general common fixed point theorem, corresponding to the fixed point theorem of Proinov [P.D. Proinov, Fixed point theorems in metric spaces, Nonlinear Anal. 64 (2006) 546-557], is presented. Examples are given to support the results. Key Words and Phrases: Common fixed points, compatible mappings, Meir-Keeler contractions, complete metric spaces. 2010 Mathematics Subject Classification: 47H10, 54H25, 54E50. Published on-line: March 1st, 2017. Abstract pdf Fulltext pdf Back to volume's table of contents