We use a hybrid iterative method to find a common element of the set of fixed points of an infinite family of Lipschitzian quasi-nonexpansive mappings, the set of solutions of the general system of the variational inequality and the set of solutions of the generalized mixed equilibrium problem in real Hilbert spaces. We also show that our main strong convergence theorem for finding that common ...

In this paper, we first introduce a new Halpern-type iterative scheme to approximate common fixed points of an infinite family of quasi-nonexpansive mappings and obtain a strongly convergent iterative sequence to the common fixed points of these mappings in a uniformly convex Banach space. We then apply our method to approximate zeros of an infinite family of accretive operators and derive a st...

In this paper, two examples of quasi-firmly type nonexpansive mappings are given to prove that the concept is different from nonexpansive mapping. Furthermore, it is studied to the convergence of the sequence of successive approximations for this class of mappings only when the super limit of iteration coefficients is less than 1. In particular, the Picard iteration {T x0} of such a mapping con...

In this paper, we introduce an iterative process which converges strongly to a common element of solutions of variational inequality problems for γ-inverse strongly monotone mappings and common fixed points of a countable family of total quasi-φ-asymptotically nonexpansive nonself mappings, and hence obtain related convergence theorems in Banach spaces. Mathematics Subject Classification: 47H09...

In this paper, we define and study convergence of an Ishikawa type iteration scheme with a new and weaker control condition for two nonself asymptotically quasi-nonexpansive mappings on a uniformly convex Banach space.

In this paper, we consider an iteration process to approximate a common random fixed point of a finite family of asymptotically quasi-nonexpansive random mappings in convex metric spaces. Our results extend and improve several known results in recent literature.

Let X be a Banach space. Let K be a nonempty subset of X. Let T : K → K be an I-asymptotically quasi-nonexpansive type mapping and I : K → K be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an I-asymptotically quasi-nonexpansive type ma...

In this paper, we first show that the iteration {xn} defined by xn+1 = P ((1−αn)xn +αnTP [βnTxn + (1− βn)xn]) converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with err...

the purpose of this paper is to study the convergence and the almost sure t-stability of the modied sp-type random iterative algorithm in a separable banach spaces. the bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure t-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. our resu...