Volume : 2, Issue : 9, SEP 2016
SUB COMPATIBLE AND SUB SEQUENTIALLY CONTINUOUS MAPS IN PROBABILISTIC METRIC SPACE
Bharat Singh, Komal Joshi
Abstract
The present paper introduces the new concepts of sub compatibility and sub sequential continuity in Probabilistic metric spaces which are weaker than occasionally weak compatibility and reciprocal continuity. We also establish a common fixed point theorem four maps using sub compatibility and sub sequential continuity.
Keywords
Probabilistic Metric spaces, weak commuting mapping, compatible mappings, common fixed point
Article : Download PDF
Cite This Article
Article No : 1
Number of Downloads : 971
References
[1] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North Holland
(Amsterdam, 1983).
[2] D. Mihet, A Generalization of a contraction principle in probabilistic metric
spaces, Part II, Int. J. Math. Math. Sci, 2005(2005),729-736.
[3] S. Banach, theories, lies, operations. Laniaries Manorial Mathematyezene, Warsaw, Poland, 1932
[4] R.P. Pant, common fixed points of non commuting mappings, J. Math .Anal. Appl. 188(1994), 436-440
[5] B.Schweizer, and A. Skalar, statistical metric spaces pacific J. Math. 10(1960), 314-334
[6] Ishak, Altun, and Duran, Turkoglu. A common fixed point theorem for a sequence of self maps in IFM-
Space, commun Korean maths, soc 21, (2006), N 4 pp, 679-687
[7] R.P. Pant, A Common Fixed Point Theorem Under a New Condition,
Indian J. Pure Appl. Math. 30 (1999), 147-152.
[8] 5. K. Menger, Statistical Metrics, Proc.Nat.Acad.Sci.U.S.A. 28 (1042),
535-537
[9] V. M. Sehgal, Some Fixed Point Theorem in Functional Analysis and
Probability, Ph.D. Dissertation, Wayne State Univ. Michigan (1966).
[10] S. Kumar and R. Chugh, common fixed point theorem using minimal
commutative and reciprocal continuity condition in metric space, Sci.
Math. Japan 56 (2002), 269-275.
[11] S. Kumar, D. B. Pant, A Common Fixed Point Theorem in Probabilistic
Metric Spaces Using Implicit Relation, Filomat 22:2 (2008),43-52.
[12] Common Fixed Point Theorem in Probabilistic Metric spaces ,G.Modi, International Mathematical Forum, Vol. 6, 2011, no. 63, 3121 – 3129.
