Menger PM-空间上复合映射不动点定理的推广

Generalization of Fixed Point Theorem for Composite Mapping on Menger PM-Space

设 (X,F,Δ)和 (Y,F,Δ)是两个完备的 Menger PM-空间 ,Δ是连续的 H型 t-范数 ,函数 Φ(t)满足条件(Φ1 ) ,本文在映射 T:X→ Y和 S:Y→ X满足更一般的条件下给出了关于复合映射 TS和 ST的不动点定理。这一定理进一步推广了 Fisher,Sehgal和 Bharucha-Reid等的有关结果 ,也是作者“Menger PM-空间上复合映射的不动点定理”一文的一般推广。最后给出了几个有用的结果作为本文主要定理的推论。

Let ( X,F,Δ) and ( Y,,Δ ) be two complete Menger PM Spaces and Δ is a continuous H type t norm; let Φ(t) be a function which satisfies condition (Φ 1 ) and let T:X→Y and S: Y→X be two mappings which satisfy certain conditions. This paper obtains a fixed point theorem for the composite mappings TS and ST . The theorem generalizes the results in 'fixed point theorem of the composite mapping on Menger PM space' of this paper. It spreads the results of Fisher, Sehgal and Bharucha Reid et al. Several useful propositions are given as corollaries of the main theorem.