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SOOCHOW JOURNAL OF MATHEMATICS

Volume 26, No. 2, pp. 103-116, April 2000




FIXED POINTS VIA $ W$-COMPATIBILITY OF TYPE (P)


BY


H. K. PATHAK AND S. N. MISHRA



Abstract. The notions of $ w$-compatible mappings of type (P) and $ w^*$-compatible mappings of type (P) for a pair of mappings have been introduced into a Hausdorff $ d$-complete topological space. It is shown that the use of the notion of $ w^*$-compatibility of type (P) is justifiable in preference to the analogous notion of weak compatibility introduced recently by Jungck and Rhoades. Subsequently, the above two notions are utilized to obtain common fixed point theorems in rather much larger class of non-metric settings. Our results improve, generalize and unify several known fixed point theorems.

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Received March 23, 1998; revised December 2, 1998 and October 21, 1999.

AMS Subject Classification. 47H10, 54H25.

Key words. fixed points, $ w$-compatibility of type (P).




chieh 2006-10-17