Affiliations: College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China
Correspondence:
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Corresponding author. Zhen-Yu Xiu, College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610000, China. E-mail: [email protected].
Note: [1] The project is supported by the National Natural Science Foundation of China (11371002), Specialized Research Fund for the Doctoral Program of Higher Education (20131101110048) and Projects (KYTZ201631, CRF201611, 17ZB0093) Supported by the Scientific Research Foundation of CUIT.
Abstract: In this paper, a new approach to Banach contraction principle in fuzzy metric space is provided. The concepts of convergent sequence, Cauchy sequence, complete metric space, contractive map and existence of fixed points, are all defined with some degrees. Adopting these degree concepts, a degree representation of Banach contradiction principle in fuzzy metric space is given by means of an inequality.
Keywords: Fixed point theorem, fuzzy metric space, Banach contraction principle
