In this paper,the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced.The fixed point theorems satisfying generalized contractive conditions are obtained,without appealing to c...In this paper,the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced.The fixed point theorems satisfying generalized contractive conditions are obtained,without appealing to completeness of X or normality of the cone.The continuity of the mapping is relaxed.Furthermore,we prove that the completeness in cone metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X.These results greatly generalize several well-known comparable results in the literature.展开更多
基金Supported by the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities'Association(202101BA070001-045)the Science and Technology Development Fund,Macao SAR(0019/2021/A1).
文摘In this paper,the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced.The fixed point theorems satisfying generalized contractive conditions are obtained,without appealing to completeness of X or normality of the cone.The continuity of the mapping is relaxed.Furthermore,we prove that the completeness in cone metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X.These results greatly generalize several well-known comparable results in the literature.
