The Existence And Convergence Of The Fixed Point For Iteration Sequence

This paper mainly studies the△-convergence and strong convergence of Ishikawa iterative sequence for nonexpansive mappings in CAT(κ) space, the△-convergence and strong convergence of the iterative sequences for a family of asymptotically non-expansive mappings in CAT(0) space, the fixed point theorems for generalized contractions in fuzzy metric space. The paper contains four parts:In chapter one, we will discuss the background of fixed point theory, main contents and significance of this paper.In chapter two, An important lemma in CAT (κ) space is obtained. Under this lemma, we study the convergence of the Ishikawa iterative sequence for non-expansive mappings. we get the results that in CAT(κ) space, the Ishikawa iterative sequence of non-expansive mappings is△-convergence to the fixed point.In chapter three, the iterative sequence of a family of asymptotically non-expansive mappings is introduced in CAT(0) space. we study the△-convergence and strong convergence of this iterative sequences. Then we prove that this iteration sequence is△-converge and strong converge to the common fixed point of the family of asymptotically non-expansive mappings respectively.In chapter four, some new contractive conditions for self-mappings is introduced in the fuzzy metric space. Under these contractive conditions, the convergence of fixed point in M-complete fuzzy metric spaces and compact fuzzy metric spaces are proved respectively and one example is given...