Strong Convergence Theorems And Common Fixed Points Theorems In Complete Metric Spaces

The problem of iteration sequence of fixed point in Hilbert space, the problem of existence of common fixed point and coupled coincidence fixed point for weak contractive mappings which satisfying certain conditions in complete metric space are discussed. The paper contains four parts as follows:In chapter one, the background of fixed point theory, main contents that we will discuss and significance are introduced.In chapter two, a new modified Mann’s iteration sequence for two finite families of asymptotically non-expansive mappings in Hilbert space is introduced. And we prove the iteration sequence converges strongly to a common fixed point of the two finite families of asymptotically non-expansive mappings in a Hilbert space. The presented theorems are generalizations of related conclusions of iteration sequences.In chapter three, common end point theorem is established for two multi-valued mappings which satisfy generalized φ-weak contractive conditions. Presented theo-rems generalized some fixed point results for single or multi-valued mappings which satisfy certain contractive factors.In chapter four, the concept of (ψ,φ)-g-weakly contractive mapping is intro-duced and four coupled coincidence point theorems for such mappings are established in an partially ordered complete metric spaces. Presented theorems are generaliza-tions of the recent coincidence fixed point theorems.