摘要
目的为了降低不动点存在性对空间完备性和映象对的连续性的要求,扩展不动点定理的使用范围。方法引进了Φ-型弱交换映象,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Φ-型弱交换的非相容映象对的公共不动点定理。结论在度量空间中,对具有Φ-型弱交换非相容映象对,在不要求空间完备性和映象的连续性的情况下能够得到了公共不动点存在性定理。
Aim To reduce the completeness of spaces and continuity of mappings in common fixed point theorem and improve the field for common fixed point theorem. Methods Ф-type weak commutativity mappings are introduced and non-compatibility of self-mapping pairs in metric spaces are applied. Results It is established that a common fixed point theorem for non-compatible mapping pairs with φ-weak contractive condition and Ф-type weak commutativity. Conclusion In metric spaces, we can obtain the only common fixed point for non-compatible mapping pairs with Ф-type weak commutativity, but not demanding for completeness of spaces and continuity of mappings. And this fixed point is discontinuous for mappings.
出处
《宝鸡文理学院学报（自然科学版）》
CAS
2008年第4期272-273,共2页
Journal of Baoji University of Arts and Sciences(Natural Science Edition)
基金
辽宁省教育厅科研资助项目(No:2005020)
关键词
度量空间
非相容映象对
争型弱交换映象
公共不动点
metric space
noncompatible mapping pairs
Ф-type weak commutativity mapping
common fixed point
