New common fixed point theorems of Greğus type for r-weakly commuting mappings in 2-metric spaces

In this paper we extend and generalize a theorem of M.R. Singh, L. S. Singh and P.P. Murthy (Common fixed points of set valued mappings, Int. J. Math. Sci., 25 (6), 411–415, 2001) in a 2-metric space with a Gregu˘s type condition, and give some common fixed point theorems of set-valued maps in 2-metric spaces.

PDF

___

[1] Abd El-Monsef, M.E., Abu-Donia, H.M. and Abd-Rabou, K.H. New types of common fixed point theorems in 2-metric spaces, Choas, Solitos and Fractals (Accepted, 2008).
[2] Broder, K.C. Fixed point theorems with applications to economics and game theory (Cambridge Univ. Press, 1990).
[3] Cho, Y. J., Khan, M. S. and Singh, S. L. Common fixed points of weakly commuting map- pings, Univ. Novomsadu, Zb. Rad. Prirod. Mt. Fak. Ser. Mat 18 (1), 129–142, 1988.
[4] Dhage, B.C. A study of some fixed point theorems (Ph.D. Thesis, Marathawada University, Aurangabad, 1984).
[5] Diviccaro, M. L., Fisher, B. and Sessa, S. A common fixed point theorem of Gregu˘s type, Publ. Math. Debrecen 34, 83–89, 1987.
[6] Fisher, B. and Sessa, S. On a fixed point theorem of Gregu˘s, Int. J. Math. Math. Sci., 9, 22–28, 1986.
[7] Gahler, S. 2-metrische Raume und ither topologische structure, Math Nachr 26, 115–148, 1963.
[8] Gahler, S. Uber die unformesior barkat 2-metriche Raume, Math Nachr 28, 235–244, 1965.
[9] Gahler, S. Zur geometrie 2-metrische Raume, Math Narchr (28, 1965) 11, 665–667, 1966.
[10] Gregu˘s, M. A fixed point theorem in Banach spaces, Bull. Univ. Math. Ital. 17(A), 193–198, 1980.
[11] Imdad, M., Khan, M. S. and Khan, M.D. A common fixed point theorem in 2-metric spaces, Math. Japonica 36 (5), 907–914, 1991.
[12] Iseki, K. A property of orbitally continuous mapping on 2-metric spaces, Math. Seminar Notes, Kobe Univ. 3, 131–132, 1975.
[13] Jungck, G. and Rhoades, B. E. Fixed points for set-valued functiond without continuity, Indian J. Pure Appl. Math., 29, 227–238, 1998.
[14] Mukherjee, R.N. and Verma, V. A note on a fixed point theorem of Gregu˘s, Mathematica Japonica 33 (5), 745–749, 1988.
[15] Murthy, P.P., Chang, S.S., Cho, Y. J. and Sharma, B.K. Compatible mappings of type (A) and common fixed point theorems, Kyungpook Math. J., 32 (2), 203–216, 1992.
[16] Murthy, P.P., Cho, Y. J. and Fisher, B. Common fixed points of Gregu˘s type mappings, Glasnik Math. 30 (50), 335–341, 1995.
[17] Naidu, S.V.R. and Prasad, J.R. Fixed point theorem in 2-metric spaces, Indian J. Pure Appl. Math., 17, 974–993, 1986.
[18] Namdeo, R.K., Dubey, S. and Tas, K. Coincidence and Fixed points of non-expansive type mappings on 2-metric spaces, Mathematical Forum 2 (16), 781–789, 2007.
[19] Singh, M.R., Singh, L. S. and Murthy, P. P. Common fixed points of set valued mappings, Int. J. Math. Sci., 25 (6), 411–415, 2001.