We prove several strong convergence theorems for the Ishikawa iterative sequence with errors to a fixed point of strictly pseudocontractive mapping of Browder-Petryshyn type in Banach spaces and give sufficient and necessary conditions for the convergence of the scheme to a fixed point of the mapping. The results presented in this work give an affirmative answer to the open question raised by Z...

In this paper, a mapping which is asymptotically hemi-pseudocontractive in the intermediate sense is introduced. Hybrid projection methods are considered for the class of mappings. Strong convergence theorems for common fixed points are established in the framework of Hilbert spaces.

Suppose that X is a arbitrary real Banach space and T : X → X is a Strongly pseudocontractive mapping. It is proved that certain Mann iterative process with random errors for the fixed point of T is stable(almost stable) with respect to T with(without) Lipschitz condition. And, two related results are obtained that deals with stability(or almost stability) of Mann iterative process for solution...

A new approximationmethod for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational ine...

In this paper, we prove some strong convergence results for a family of three generalized strongly Φ-pseudocontractive (accretive) mappings in Banach spaces. Our results are generalizations and improvements of convergence results obtained by several authors in literature. In particular, they generalize and improve the results of Olaleru and Mogbademu [17], Xue and Fan [22] which is in turn a co...

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.

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...

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...