IJPAM: Volume 109, No. 4 (2016)
Department of Mathematics
School of Advanced Sciences,
Vellore-632014, Tamil Nadu, INDIA
Abstract. Let be a -metric space, , a self-map on and . Some misconceptions are brought about in findings of Mustafa et al , and a fixed point theorem for a Chatterjee-type -contraction on a complete -metric space is proved. More over, the unique fixed point p will be its contractive fixed point, in the sense that for each each , the -iterates converge to .
Received: Jule 2, 2016
Revised: September 13, 2016
Published: October 9, 2016
AMS Subject Classification: 54H25
Key Words and Phrases: -metric space, Chatterjee-type -contraction, fixed point, -contractive fixed point
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- S.K. Chatterjea, Fixed-point theorems, C.R. Acad. Bulgare Sci., 25 (1972), 727-730, MR 48#2845.
- Z. Mustafa, H. Obiedat, F. Awawdeh, Some fixed point theorems for mapping on complete G-Metric Spaces, Fixed Point Theory and Applications (2008), Article ID 189870, 1-12, doi: 10.1155/2008/189870.
- Z. Mustafa, B. Sims, A new approach to generalized metric spaces, Jour. Nonlinear and Convex Anal., 7, No. 2 (2006), 289-297.
- T. Phaneendra, K. Kumara Swamy, Unique fixed point in G-metric space through greatest lower bound properties, Novi Sad J. Math., 43 (2013), 107-115.
DOI: 10.12732/ijpam.v109i4.3 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 789 - 798
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