ON VARIOUS TYPES OF COMPATIBLE MAPS AND COMMON FIXED POINT THEOREMS FOR NON-CONTINUOUS MAPS

Authors : M.r. SİNGH, Y. Mahendra SİNGH

Pages : 503-513

View : 13 | Download : 7

Publication Date : 2011-04-01

Article Type : Research Paper

Abstract :Concepts of S- and A- compatible of type insert ignore into journalissuearticles values(E);, S- and A- reciprocally continuous are introduced. In this paper, we give a brief discussion on various types of compatible maps and obtain some common fixed point theorems for non-continuous self maps on a metric space. Here the utility of the newly introduced maps viz. S- compatible of type insert ignore into journalissuearticles values(E); and S- reciprocally continuous insert ignore into journalissuearticles values(one sided); in lieu of continuity is shown. Our results improve, generalize or extend the results of H. Bouhadjera insert ignore into journalissuearticles values(General common fixed point theorem for compatible mappings of type insert ignore into journalissuearticles values(C);, Sarajevo J. Math. 1 insert ignore into journalissuearticles values(14);, 261–270, 2005);, X. P. Ding insert ignore into journalissuearticles values(Some common fixed point theorems of commuting mappings II, Math.Seminar Note 11, 301–305, 1983);, M. L. Diviccaro and S. Sessa insert ignore into journalissuearticles values(Some remarks on common fixed points of four mappings, Jnanabha 15, 139– 149, 1985);, G. Jungck insert ignore into journalissuearticles values(Compatible mappings and common fixed points insert ignore into journalissuearticles values(2);, Internat. J. Math. & Math. Sci. 11 insert ignore into journalissuearticles values(2);, 285–288, 1988);, S.M. Kang, Y. J. Cho and G. Jungck insert ignore into journalissuearticles values(Common fixed points of compatible mappings, Internat. J. Math. & Math. Sci. 13 insert ignore into journalissuearticles values(1);, 61–66, 1990);, V. Popa insert ignore into journalissuearticles values(Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstr. Math. 32insert ignore into journalissuearticles values(1); insert ignore into journalissuearticles values(1999);, 157–163, 1999);, and others.
Keywords : Compatible maps, Compatible of type E, , S and A compatible of type E, , S and A reciprocally continuous, Weakly compatible maps and common fixed points, 2000 AMS C