In this paper we elaborate new methods to the theory of parametric generalized equations governed by accretive mappings. Two implicit function theorems will be proved, one for m-accretive and another for locally accretive and continuous set-valued mappings. Making use of the theorem for m-accretive mappings we will study parametric nonlinear evolution problems. It will be also shown that there ...

⟨(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...

For a countable family {Tn}n 1 of strictly pseudo-contractions, a strong convergence of viscosity iteration is shown in order to find a common fixed point of {Tn}n 1 in either a p-uniformly convex Banach space which admits a weakly continuous duality mapping or a p-uniformly convex Banach space with uniformly Gâteaux differentiable norm. As applications, at the end of the paper we apply our res...