Abstract
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.
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Acknowledgement
We are grateful to the editor and the anonymous referees for their valuable comments and useful suggestions, which improve the original manuscript greatly.
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Conflict of interest The authors declare no conflict of interest.
Supported by the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities’ Association(202101BA070001-045) and the Science and Technology Development Fund, Macau SAR(0019/2021/A1).
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Han, Y., Xu, Sy. & Ma, C. Generalized Kannan-type contraction and fixed point theorems. Appl. Math. J. Chin. Univ. 38, 235–247 (2023). https://doi.org/10.1007/s11766-023-4093-1
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DOI: https://doi.org/10.1007/s11766-023-4093-1
Keywords
- cone metric spaces over Banach algebras
- generalized Kannan-type contraction
- completeness
- asymptotic regularity
- fixed point