锥度量空间中满足φ压缩的一族映射的公共不动点定理.pdf

应 用 数 学 M ATHEMATICA APPLICATA 2015，28(4)：782—792 Fixed PointTheorem sof 一contraction raFam ily ofM appingsin Cone M etricSpaces HANfan(艳)，XUShaOyuan(许绍元) (1．SchoolofMathematicsandStatisticsZhaotongUniversity,Zhaotong657000China； 2．SchoolofMathematicsandStatistics，HanshanNormalUniversity，Chaozhou 521041，China) Abstract： In thispaper，wedefinetheconceptofweakly ~-contraction and obtain ， colnn2onfixedpointtheoremsforthreemappingsandafamilyofmappings．Themappings arenotnecessarily continuousand thecone isnotassumed to be norma1．Theseresults generalizeseveralwell—knowncomparableresults．M oreover，anexampleisgiventosupport ournew results． Keywords：Conemetricspace；Weakly~-contraction；Commonfixedpoint CLCNumber：0177．91 AMS(2000)Subjectclassification：54H25：47It10 Documentcode：A ArticleID2015)04-0782—11 1．Introduction and Prelim inaries Thestudyofcommonfixedpointsofmappingssatisfyingcertaincontractiveconditions hasbeen discussedbymany authorssinceitwasintroduced in 1976．becauseithasnot only importanttheoreticalmeaning butalso wideapplications[1-6] ． Recently,HUANG and ZHANG I【Jintroducedtheconceptofconemetricspaceasageneralizationofmetricspace ． Theyproved thepropertiesofsequencesin conemetricspacesandobtainedvariousfixed pointtheoremsforcontractivemappings．Afterwards，AbbasandJungck[。1established the common fixedpointsfortwomappingswithoutexploitingthenotion ofcontinuity．Since then，corrlrnonfixedpointthe