In this article, we prove strong convergence of sequence generated by the following iteration sequence for a class of Lipschitzian pseudocontractive mapping T: x n+1 = β n u + (1 − β n)[α n Tx n + (1 − α n)x n ] whenever {a n } and {b n } satisfy the appropriate conditions.

and Applied Analysis 3 It is clear that 1.7 is equivalent to 〈 Sx − Sy, x − y ≤ ∥x − y∥2, ∀x, y ∈ C. 1.8 The class of κ-strict pseudocontractions which was introduced by Browder and Petryshyn 17 in 1967 has been considered by many authors. It is easy to see that the class of strict pseudocontractions falls into the one between the class of nonexpansive mappings and the class of pseudocontractio...

We introduce an iterative scheme for finding a common element of the set of fixed points of a kstrictly pseudocontractive mapping, the set of solutions of the variational inequality for an inversestrongly monotone mapping, and the set of solutions of the mixed equilibrium problem in a real Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common elem...

and Applied Analysis 3 Theorem 1.3. Let E be a real q-uniformly smooth Banach space which is also uniformly convex, let C be a nonempty closed convex subset of E, let T : C → C be a (λ, {kn})-strictly asymptotically pseudocontractive mapping such that ∑∞ n 1 k 2 n − 1 < ∞, and let F T / ∅. Let {αn} ⊂ 0, 1 be a real sequence satisfying the following condition: 0 < a ≤ αn ≤ b < q 1 − k 2cq 1 L − ...

‎a new approximation method for the set of common fixed points of‎ ‎nonexpansive mappings and the set of solutions of systems of‎ ‎variational inequalities is introduced and studied‎. ‎moreover‎, ‎we‎ ‎apply our main result to obtain strong convergence theorem to a‎ ‎common fixed point of a nonexpannsive mapping and solutions of ‎a ‎system of variational inequalities of an inverse strongly mono...

We introduce a new iterative algorithm for finding a common element of the solution set of the variational inequality problem for a continuous monotone mapping, the zero point set of a maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the sequence generated by the proposed algorithm to a commo...

In this paper, we introduce two iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of a general system of variational inequalities for continuous monotone mappings and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. First, this system of variational inequalities is proven to be equivalent to...