Resultate der Mathematik, Vol. 6 (1983) 0378-6218/83/020202-05$01.50 + 0.20/0 © 1983 Birkhauser Verlag, Basel Fixed point theorems in uniform spaces S. L. SINGH and S. N. MISHRA Abstract. Fixed point theorems in a Hausdorff uniform space are proved by considering a contractive type condition for a triplet of mappings. AMS(MOS) subject classifications (1980). Primary 54H25; Secondary 54E15. 1. Introduction Let (X, CU) be a uniform space. A family {d",: A E I} of pseudometrics on X is called an associated family for the uniformity CU on X if the family B = {V(""r) : A E I, r > O} is a subbase for the uniformity au, where V("'.r) = {(x, y)EXxX:d",(x, y)<r}. We may assume B itself to be a base for OU by adjoining the finite intersection of members of B, if necessary. The corresponding family of pseudometrics is called an augmented associated family for CU. An associated family and an augmented associated family for CU will be denoted by D and D* respectively. For details the reader is referred to Tarafdar [4] and Thron [5]. Let P, Q and T be mappings from a uniform space X to itself such that d",(Px, Qy)::::;;a",d",(Tx, Ty)+b",d",(Px, Tx)+c",d",(Qy, Ty) +e",d",(Px, Ty)+f",d",(Qy, Tx) for all x, y E X, A E I, a"" b"" c"', e", and f", being non-negative real numbers. (1.1) The triplet (P, Q, T) satisfying (1.1) will be called "generalized Jungck con- traction" on X provided (1.2) For a pair of Jungck mappings we refer to Singh [3]. In section 2 of the present note we prove common fixed point theorems for a generalized Jungck contraction (P, Q, T). In section 3 we study the relationship between the convergence of three sequences of mappings and the convergence of their common fixed points. 202