Abstract
We extend the notion of R-weak commutativity and its variants to probabilistic metric spaces and prove common fixed point theorems concerning them. Examples are included to reflect upon the distinctiveness of the types of mappings defined in the paper.
Similar content being viewed by others
References
G. Bocşan, On some fixed point theorems in probabilistic metric spaces, Seminar on the Theory of Functions and Applied Mathematics, A: Probabilistic Metric Spaces, No. 24, Univ. of Timişoara (1974).
G. L. Cain and R. H. Kasriel, Fixed and periodic points of local contraction mappings on probabilistic metric spaces, Math. Systems Theory, 9 (1976), 289–297.
V. I. Istrăteşcu and E. Roventa, On fixed point theorems for mappings on probabilistic metric spaces, Seminar on the Theory of Functions and Applied Mathematics, A: Probabilistic Metric Spaces, No. 19, Univ. of Timişoara (1974).
V. I. Istrăteşcu and I. Săcuiŭ, Fixed point theorems for contraction mappings on probabilistic metric spaces, Rev. Roumaine Math. Pures. Appl., 18 (1973), 1375–1380.
G. Jungck, Commuting mappings and fixed point, Amer. Math. Monthly, 83 (1976), 261–263.
R. Pant, Common fixed points of non-commuting mappings, J. Math. Anal. and Appl., 188 (1994), 436–440.
H. K. Pathak, Y. J. Cho and S. M. Kang, Remarks on R-weakly commuting mappings and common fixed point theorems, Bull. Korean Math. Soc., 34 (1997), 247.
B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North Holland (Amsterdam, 1983).
B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. of Math., 10 (1960), 313–324.
V. M. Sehgal, Some fixed point theorems in functional analysis and probability, Ph.D. Dissertation, Wayne State Univ. Michigan (1966).
V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings on probabilistic metric spaces, Math. Systems Theory, 6 (1972), 97–102.
S. Sessa, On weak commutativity conditions of mappings in fixed point consideration, Publ. Inst. Math. Beograd, 32(46) (1982), 149–153.
H. Sherwood, Complete probabilistic metric spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 20 (1971), 117–128.
S. P. Singh and B. A. Meade, On common fixed point theorems, Bull. Austr. Math. Soc., 16 (1977), 49–53.
S. L. Singh, B. D. Pant and R. Talwar, Fixed points of weakly commuting mappings on Menger spaces, Jnanabha, 23 (1993), 115–122.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kohli, J.K., Vashistha, S. Common fixed point theorems in probabilistic metric spaces. Acta Math Hung 115, 37–47 (2007). https://doi.org/10.1007/s10474-006-0533-7
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10474-006-0533-7
Key words and phrases
- fixed point
- Menger space
- probabilistic metric space
- R-weakly commuting mappings
- R-weakly commuting mappings of types (i), (ii) and (iii)