局部化单调原理及应用

以下我们总假定(X,d)表度量空间,简记为X,T为X的自映象,B:X?R_+~0=0,+∞)。我们称X满足广义TCS收敛条件,若存在一点x_0∈X使得{B(T~nx_0)}收敛,蕴含{T~nx_0}有一个收敛子列。称σ(x,T)={x,T_x,T~2x,…,T~nx,…}为x的T轨道。称函数B(x)在p∈X点轨道连续,若{x_n}?σ(x,T),x_n→p,有B(x_n)?B(p)。若B(x)在X内每一点轨道连续,称B(x)在X上轨道连续。我们有如下结果。

Locally Monotone Principles With Applications

In this paper, two generalized results are established, that is,locally mono-tone principle and locally monotone principle in a compact metric space. As an application, two new fixed point theorems of B. E. Rhoades'1] (25) type mapping and a new fixedpointtheorem of (3) type mapping are given and a some results of2.3.4.5.6.] are generalized.