Research On Some Problems Of Cyclic And Non-cyclic Contraction Mappings In Generalized Metric Spaces

Research on cyclic and non-cyclic contractive mappings is an important component of nonlinear functional analysis,which is widely applied to many branches of mathematics.In this thesis,we study the fixed point theorems for cyclic and non-cyclic contraction mappings in generalized metric spaces and their applications.The full text is divided into four chapters.In chapter one,we introduce the development of fixed point theory in generalized metric spaces.And we give some definitions and related concepts of generalized metric spaces.In chapter two,some new theorems for various cyclic contractions in G_b-metric spaces are established,which generalize some famous results in corresponding articles.On the other hand,the notion of a cyclic ?-??-contractive mappings in G_b-metric spaces is introduced,and a new fixed point theorem is proved.Moreover,we give some applications and examples to support our main results.In chapter three,we put forward the concept of G_bl-metricspaces.Furthermore,we establish a new common fixed point theorem for cyclic ?-?-contraction in G_bl-metric spaces.As consequences,we obtain some fixed point theorems for non-cyclic contraction mappings in the G_bl-metric spaces and G-metric spaces.In chapter four,some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces.As an application,we discuss the existence of the solutions for a class of nonlinear integral equations.