Convergence theorems for fixed points of uniformly continuous Φ-pseudo-contractive-type operator
C.E. Chidume, Ngalla Djitté, JEREMIAH NKWEGU EZEORA · Fixed Point Theory and Applications · 2013
Let E be a real normed linear space, let K be a nonempty convex subset of E, and let be a uniformly continuous Φ-pseudo-contractive-type mapping. It is proved that both the Mann-type and Ishikawa-type iteration schemes converge strongly to the unique fixed point of T, without requiring that the sequences associated with the schemes be bounded. Our theorems are significant improvements on the results of Chang et al. (Iterative methods for nonlinear operators in Banach spaces, 2002), those of Gu (Northeast Math. J. 17(3):340-346, 2001), and those of a host of other authors. MSC:47H06, 47H09, 47J05, 47J25.