Occasionally weakly compatible mappings and common fixed points in menger space

Abstract views: 30 / PDF downloads: 41


  • Ajay Kumar Chaudhary Department of Mathematics, Trichandra Multiple Campus, Tribhuvan University, Ghantaghar, Kathmandu, Nepal


Menger Space, compatible mappings, weakly compatible mappings, occasionally weakly compatible. Mathematics Subject Classification (1991): 47H10, 54H25


The purpose of this paper is to establish a common fixed point result in Menger space in two pairs and three pairs of self mappings by using occasionally weakly compatible mappings. Our first theorem generalizes the theorem of Sharma and Shahu [1] and B. Fisher et al. [2] and both theorems deduce some similar results in the literature.


B. K. Sharma, N. K. Sahu, Common fixed point theorem of three continuous mappings, Math. Student., 1991, 59: 77–80.

T. Mustafa, K. Tas, B. Fisher, Common fixed point theorems for compatible mappings, Internat. J. Math. and Math. Sci., 1996, 19(3): 451–456.

K. Menger, Statistical Matrices, Proceedings of National Academy of Sciences of USA., 1942, 28: 535–537.

V. M. Sehgal, A. T. Bharucha-Reid, Fixed Point contraction mapping in Probabilistic Metric Space, Math System Theory., 1972, 6: 97–102.

A. T. Bharucha Reid, Fixed point theorem in Probabilistic analysis, Bull. Amer. Math. Soc., 1976, 82(5): 641–657.

Gh. Bosscan, On some common fixed point theorem in Probabilistic metric spaces, Math Balkamkau, 1974, 60–70.

S-S. Chang, On some common fixed point theorem in probabilistic metric space and its applications, Z. Wahrscheinlichkeilichkeitstheorie verw. Gebiete., 1983, 63: 463–474.

A. K. Chaudhary, K. B. Manandhar, K. Jha, P. P. Murthy, A common fixed point theorem in Menger space with compatible mapping of type (P), International Journal of Math. Sci. and Engg. Appls., 2021, 15(2): 59–70.

Y. J. Cho, P. P. Murthy, M. Stojakovic, Compatible Mappings of type (A) and Common fixed point in Menger space, Comm. Korean Math. Soc., 1992, 7(2): 325–339.

O. Hadzic, A fixed point theorem in Menger space, Publ. Inst. Math. Beograd, 1979, 20(40): 107–112.

O. Hadzic and E. Pap, Fixed-Point Theory in Probabilistic Metric Space, Kluwer Academic Publisher, London, 2010, pp. 536.

T. L. Hicks, Fixed point theory in probabilistic metric spaces, review of research,, Fac.Sci. Math. series, Univ. of Novi Sad., 1983, 13: 63–72.

I. Istratescu, A common fixed point theorem for mappings with a probabilistic Contractive, Rev. Roumaine Math. Pures Appl., 1981, 26: 431–435.

G. Jungck, P. P. Murthy, Y. J. Cho, Compatible mappings of type (A) and common fixed points, Math. Japonica., 1993, 38: 381–390.

H. K. Pathak, Y. J. Cho, S. S. Chang and S. M. Kang, Compatible mappings of type (P) and fixed point theorem in metric spaces and Probabilistic metric spaces, Novi Sad J. Math., 1996, 26(2): 87–109.

B. E. Rhoades, G. Jungck, Fixed point theorem for occasionally weakly compatible mappings in metric space, Fixed point theory., 2006, 7: 280–296.

B. Schweizer, A. Sklar, Statistical metric space, Pacific J. of Math., 1960, 10: 314–334.

H. Sherwood, Complete probabilistic metric spaces, Z. Wahrscheinlichkeilichkeitstheorie verw. Gebiete., 1971, 20: 117–128.

A. Razani, A fixed point theorem in the Menger probabilistic metric space,New Zealand J. Math., 2004, 35: 109–114.

A. Razani, Existence of fixed point for the non-expansive mapping of intuitionistic fuzzy metric spaces, Chaos, Solitons, and Fractals., 2006, 30: 367–373.

S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math., Beograd, 1982, 32(46): 149–153.

G. Jungck, Compatible Mapping and common fixed points, Internat. J. Math. Sci., 1986, 9(4): 771–779.

G. Jungck, Common fixed points for non-continuous non self-maps on non-metric spaces, Far East. J. Math. Sci., 1996, 4(2): 199–212.

B. Singh, S. Jain, Common Fixed Point theorem in Menger Space through Weak Compatibility, J. Math. Analy. Appl., 2005, 301: 439–448.

S. N. Mishra, Common fixed points of Compatible Mappings in probabilistic Metric Space, Math. Japonica., 1991, 36: 283–289.

N. Shahzad, M. A. Thapagi, Generalized I-Non-expensive self-maps and Invariants Approximations, Acta Mathematica Sinica, English Series., 2008, 24(5): 867–876.

B. D. Pant, S. Chauhan, S. Kumar, Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces, J. Adv. Research Pure Math., 2011, 3(4): 17–23.

B. Schweizer, A. Sklar, Probabilistic Metric space., Dover Publications, INC, Mineola, New York, 2005.

E. P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publisher, Amsterdam, 2000.

A. Rani, S. Kumar, Some common fixed point theorem in Menger Space, J. of Applied Math., 2012, 3: 235–245.

U. Rajopadhyaya, K. Jha, M. Imdad, Fixed point theorem for occasionally weakly compatible mappings in semi metric space, A. of Pure and Appl. Math., 2014, 5(2): 153–157.




How to Cite

Ajay Kumar Chaudhary. (2023). Occasionally weakly compatible mappings and common fixed points in menger space. Results in Nonlinear Analysis, 6(4), 47–54. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/328