The convergence theorems of Ishikawa iterative process with errors for Φ-hemi-contractive mappings in uniformly smooth Banach spaces
Zhiqun Xue, Guiwen Lv, BE Rhoades · Fixed Point Theory and Applications · 2012
Let D be a nonempty closed convex subset of an arbitrary uniformly smooth real Banach space E, and be a generalized Lipschitz Φ-hemi-contractive mapping with . Let , , , be four real sequences in and satisfy the conditions (i) as and ; (ii) . For some , let , be any bounded sequences in D, and be an Ishikawa iterative sequence with errors defined by (1.1). Then (1.1) converges strongly to the fixed point q of T. A related result deals with the operator equations for a generalized Lipschitz and Φ-quasi-accretive mapping. MSC:47H10.