The Fixed Point Theorem Of Compressed Mapping In Fuzzy Metric Space

Based on the previous theoretical results,we introduce many kinds of contractive mappings in fuzzy metric spaces,and study their fixed point problems systematically.This article is divided into six chapters.In the first and second chapters,in order to generalize ?-weakly contractive mapping and(?,?)-almost weakly contractive mapping in fuzzy metric space,they introduce the definition of cyclic generalized(?,?)-weakly contractive mapping and cyclic generalized(?,?)-almost weakly contractive mappings in fuzzy metric spaces respectively.And they study the fixed point theory of the two kinds of mappings by iterative and inverse methods respectively.And the correctness and feasibility of the theorems are illustrated by the examples.In the third chapter,it proposes the concept of fuzzy generalized H-weak contractive mapping in fuzzy metric space,which optimizes the definition of fuzzy H-weak contractive mapping.And it proves the fixed point's existence and uniqueness of the mapping by the iterative and inverse method.In the fourth chapter,inspired by the definition of(?,?)-admissible Geraghty type contractive mappings in metric space,it introduces the concept of(?,?)-admissible Geraghty type contractive mappings in fuzzy metric space.And it proves the existence and uniqueness of the fixed point by iterative and inverse methods.And the feasibility of the theorem is illustrated with an example.Inspired by cyclic ?-contractive mapping and contractive mapping in metric space,the fifth chapter and the sixth chapter introduce the concepts of cyclic?-contractive mapping and generalized contractive mapping in non Archimedes fuzzy metric space respectively,and study the fixed point problem by using the methods of inverse and classification.