The convergence theorems of Ishikawa iterative process with errors for Φ-hemi-contractive mappings in uniformly smooth Banach spaces

Let D be a nonempty closed convex subset of an arbitrary uniformly smooth real Banach space E, and T : D -> D be a generalized Lipschitz Phi-hemi-contractive mapping with q is an element of F(T) not equal empty set. Let {a(n)}, {b(n)}, {c(n)}, {d(n)} be four real sequences in [0, 1] and satisfy the conditions (i) a(n), b(n), d(n) -> 0 as n -> infinity and c(n) = o(a(n)); ( ii) Sigma(infinity)(n=0) a(n) = infinity. For some x(0) is an element of D, let {u(n)}, {v(n)} be any bounded sequences in D, and {x(n)} 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 Phi-quasi-accretive mapping.