Common fixed point results for three maps in generalized metric space

• Published in: Advances in difference equations Vol. 2011; no. 1; pp. 1 - 20
• Main Authors: Abbas, Mujahid, Nazir, Talat, Saadati, Reza
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 31.10.2011; Springer Nature B.V
• Subjects: Analysis; Classification; Continuity; Difference and Functional Equations; Fixed points (mathematics); Functional Analysis; Mapping; Mathematical analysis; Mathematics; Mathematics and Statistics; Metric space; Ordinary Differential Equations; Partial Differential Equations; Probability theory; Theorems; common fixed point; generalized metric space
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/1687-1847-2011-49

Mustafa and Sims [Fixed Point Theory Appl. 2009 , Article ID 917175, 10, (2009)] generalized a concept of a metric space and proved fixed point theorems for mappings satisfying different contractive conditions. In this article, we extend and generalize the results obtained by Mustafa and Sims and prove common fixed point theorems for three maps in these spaces. It is worth mentioning that our results do not rely on continuity and commutativity of any mappings involved therein. We also introduce the notation of a generalized probabilistic metric space and obtain common fixed point theorem in the frame work of such spaces. 2000 Mathematics Subject Classification : 47H10.