完备度量空间中四个映象的一个新的不动点定理

A new fixed point theorem in complete metric spaces for four mappings

目的为了降低公共不动点定理中对映象对相容性的要求,扩展不动点定理的应用范围。方法利用度量空间中映象对相容和次相容的条件进行研究。结果在完备度量空间建立了一个新的公共不动点定理。结论结果表明:完备度量空间中四个映象在如下压缩条件下,x,y∈X,有d(Sx,Ty)≤f[d(Sx,Ax),d(Ty,By)]+ad(Sx,By)+bd(Ty,Ax)+cd(Ax,By),其中a,b,c∈[0,∞)且a+b+c<1,f:[0,∞)×[0,∞)→[0,∞);可以把相容性条件部分地放宽到次相容的情况,推广和统一了已有文献的相关结果。

Aim To reduce the compatibility of mappings in common fixed point theorem and improve the field for common fixed point theorem. Methods It is used that the compatibility and subcompatibility of self-mapping pairs in complete metric spaces. Results Constructing a new common fixed point theorem for four mappings in complete metric spaces. Conclusion The results shows that： in complete metric spaces, under the contractive condition i. e.x,y∈X, we have d（Sx,Ty）≤f[d（Sx,Ax）,d（Ty,By）]＋ad（Sx,By）＋bd（Ty,Ax）＋cd（Ax,By）, where a,b,c∈[0,∞） and a＋b＋c〈1,f：[0,∞）×[0,∞）→[0,∞）; we can lessen the compatible conditions, the main results in related literatures are generalized and unified.