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In this article, we propose a Halpern-type subgradient extragradient algorithm for solving a common element of the set of solutions of variational inequality problems for continuous monotone mappings and the set of f-fixed points of continuous f-pseudocontractive mappings in reflexive real Banach spaces. In addition, we prove a strong convergence theorem for the sequence generated by the algorithm. As a consequence, we obtain a scheme that converges strongly to a common f-fixed point of continuous f-pseudocontractive mappings and a scheme that converges strongly to a common zero of continuous monotone mappings in Banach spaces. Furthermore, we provide a numerical example to illustrate the implementability of our algorithm.

The purpose of this article is to study the method of approximation for zeros of the sum of a finite family of maximally monotone mappings and prove strong convergence of the proposed approximation method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems and provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

In this paper, we construct a Halpern-type subgradient extragradient iterative algorithm which converges strongly to a common point of the f-fixed point set of a continuous f-pseudocontractive mapping and the solutions set of a variational inequality problem for Lipschitz monotone mapping in reflexive real Banach spaces. In addition, a numerical example is given to demonstrate the behaviour of the convergence of the algorithm. Our results improve, generalize and unify some related recent results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the method of approximation for zeros of the sum of a finite family of maximal monotone mappings in the setting of Banach spaces. Under some mild conditions, we establish strong convergence results of the proposed approximation method. The assumptions that one of the mappings is single valued and α-inverse strongly monotone are dispensed with. In addition, we give some applications to the minimization problems. Finally, we provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings. [ABSTRACT FROM AUTHOR]

Let K be a nonempty closed convex and bounded subset of a real Banach space E. Let T: = {T(t): t ∈ +} be a strongly continuous semigroup of asymptotically nonexpansive self-mappings on K with a sequence {Lt} ⊂ [1, ∞). Then, for a given u0 ∈ K and sn ∈ (0, 1), tn > 0 there exists a sequence {un} ⊂ K such that un = (1 - αn)T(tn)un + αnu0, for each n ∈ , satisfying | un - T(t)un | → 0 as n → ∞, for any t ∈ +, where [image omitted]. If, in addition, E is uniformly convex with uniformly G[image omitted]teaux differentiable norm, then it is proved that F(T) ≠ ∅ and the sequence {un} converges strongly to a point of F(T) under certain mild conditions on {Lt}, {tn} and {sn}. Moreover, it is proved that an explicit sequence {xn} generated from x1 ∈ K by xn+1: = αnu0 + (1 - αn)T(tn)xn, n ≥ 1, converges to a fixed point of T under appropriate assumption imposed upon the sequence {xn}. [ABSTRACT FROM AUTHOR]