(A_g)型相容映象的公共不动点定理

A Common Fixed Point Theorem for (A_g) Type Compatible 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。方法引进(Ag)型相容映象,再利用度量空间中自映象对的非相容性条件。结果建立了一类具有Φ-压缩条件和(Ag)型相容性的两对非相容映象对的公共不动点定理。结论结果表明:度量空间中,对于具有(Ag)型相容性的非相容映象对,在不要求空间完备和映象连续的情况下就能够得到唯一的公共不动点,并且这个不动点是映象的不连续点。

Aim To reduce the compatibility of mappings in common fixed point theorem and improve the field for common fixed point therorem. Methods Introducing （A,） type compatible mappings and applying non-compatibility of self-mapping pairs in metric spaces. Results Constructing a common fixed point theorem for non-compatible mappings with φ-contractive condition and （Ag） type compatibility. Conclusion The results shows that： in metric spaces, we can obtain the only common fixed point for non-compatible mapping with （Ag） type compatibility, but not demanding for completeness of spaces and＇continuity of mappings. And this fixed point is discontinuous for mappings.