Keywords:-
Article Content:-
Abstract
The aim of this paper is to establish a common fixed point theorem for expansion mappings involving six mappings in a Menger space, utilizing the concepts of semi-compatibility and weak compatibility while considering the continuity of the mappings.
References:-
References
Ajay Kumar Chaudhary, Chet Raj Bhatta and Dilip Kumar Sah, Menger Space and Some Contraction Mappings, Applied Nonlinear Analysis, Vol 3 No.7, 641-648 (2024).
Constantin , G., I.Istratescu, Elements of probabilistic Analysis, Ed. Acad. Bucuresti and Kluwer Acad. Publ.,1989.
Fang J.X. , Common fixed point theorems of compatible and weakly compatible maps in Menger space., Nonlinear Analysis : Theory , method and Application , Vol.71 , No. 5-6 , 2009, PP. 1833-1843.
Hicks, T.L., Fixed point theory in probabilistic metric spaces, Rev. Res. Novi Sad, 13(1983), 63-72.
Istratescu, I., On some fixed point theorems in generalized Manger spaces, Boll. Un. Mat. Ital., 5 (13-A) (1976),95-100.
Istratescu, I., On generalized complete probabilistic metric spaces, Rev. Roum. Math. Pures Appl. XXV(1980), 1243-1247.
Jungck, G., Commuting mappings and fixed points, Amer. Math. Monthly, 83 (1976),261-263.
Jungck, G., Compatible mappings and common fixed points, Internat. J.math.Sci., 9(1986),771-779.
Jungck, G, Some fixed point theorems for compatible maps, Internat. J. Math. & Math. Sci., 3 (1993),417-428.
Kumar, S., Common fixed point theorems for expansion mappings in various spaces, Acta Math.Hungar, 118(1-2), 9-28(2008).
kutukcu, S., On common fixed point in Menger probabilistic metric spaces , Int. J. Cont. Math. Sci. 2(2007) 8, 382-391.
Menger, K., Statistical metric , Proc. Nat.Acad.,28 (1942),535-537.
Mishra, S.N., Common fixed points of compatible mappings in PM-spaces, ic spaces, Math. Japon., 36 (1991), 283-289.
Pant B.D. and Chauhan S., A Contraction theorem in menger space using weak compatibility, Int. J. Math. Sci. & Engg. Appls. 4(2010), 177-186.
Popa, V.; Fixed point theorems for expansion mappings, “Babes Bolyai” univ.,Res.Sem.3,(1987),25-30
Popa, V., Fixed points for non-surjective expansion mappings satisfying an implicit relation, B. fascicola Mathematica Informatics, vol.18(1), 15-108 (2002).
Rhoades, B.E., Generalized contractions, Bull. Calcutta Math. Soc., 71, 323-330 (1979).
Sehgal, V.M., Bharucha A.T.-Reid, Fixed point of contraction mapping on PM spaces, Math. Systems Theory, 6 (1972), 97-100.
Sessa, S., On a weak commutative condition in fixed point consideration, Publ. lnst. Math., 32 (1982) 146-153.
Singh, B.,Jain, S., A fixed point theorem in Menger Space through weak compatibility, J. Math. Anal. Appl., 301 (2005), 439-448.
Singh, S.P. and Meade, B.A., On common fixed point theorem, Bull. Aust. Mat. Soc.,16(1977),49-53.
Schweizer, B., Sklar, A., Probabilistic Metric Spaces, North- Holland, Amsterdam, 1983.
Tardiff, R.M., Contraction maps on probabilistic metric spaces, J. Math. Anal. Appl. 165 (1992), 517-523.
Singh, B.,Jain, S., A fixed point theorem in Menger spaces through weak compatibility, J. Math. Anal. Appl. 301(2005) 439-448.
Verma et.al. Common fixed point theorems for weakly compatible mappings on Menger spaces and application, Int.Journal of Math.Analysis, Vol.71,No.5-6, 2009, PP. 1833-1843.