Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...

⟨(I − T) x − (I − T) y, j (x − y)⟩ ≥ k 󵄩󵄩󵄩󵄩x − y 󵄩󵄩󵄩󵄩 2 (4) for all x, y ∈ D(T), where k = (t − 1)/t ∈ (0, 1). Consequently, from inequality (4) it follows easily that T is strongly pseudocontractive if and only if 󵄩󵄩󵄩󵄩x − y 󵄩󵄩󵄩󵄩 ≤ 󵄩󵄩󵄩󵄩x − y + s [(I − T − kI) x − (I − T − kI) y] 󵄩󵄩󵄩󵄩 (5) for all x, y ∈ D(T) and s > 0. Closely related to the class of pseudocontractive maps is the class of accret...

In this paper‎, ‎strong convergence theorems of Ishikawa type implicit iteration‎ ‎process with errors for a finite family of asymptotically‎ ‎nonexpansive in the intermediate sense and asymptotically‎ ‎quasi-pseudocontractive type mappings in normed linear spaces are‎ ‎established by using a new analytical method‎, ‎which essentially‎ ‎improve and extend some recent results obtained by Yang‎ ‎...

‎In a real Hilbert space‎, ‎an iterative scheme is considered to‎ ‎obtain strong convergence which is an essential tool to find a‎ ‎common fixed point for a countable family of nonexpansive mappings‎ ‎and the solution of a variational inequality problem governed by a‎ ‎monotone mapping‎. ‎In this paper‎, ‎we give a procedure which results‎ ‎in developing Shehu's result to solve equilibrium prob...