and Applied Analysis 3 Then (a) for any L ∈ (N,M), there exist θ ∈ (0, 1) and T ≥ n 0 + τ + β such that for each x 0 = {x 0n } n∈N β ∈ A(N,M), the Mann iterative sequence with errors {x m } m∈N 0 = {x mn } (m,n)∈N 0 ×N β generated by the scheme

We prove some existence theorems for solutions of a certain system of multivariate nonexpansive operator equations and calculate the solutions by using the generalized Mann and Halpern iterative algorithms in uniformly convex and uniformly smooth Banach spaces. The results of this paper improve and extend the previously known ones in the literature.

In this paper, we study the existence of solutions for fractional evolution equations with nonlocalconditions. These results are obtained using Banach contraction xed point theorem. Other resultsare also presented using Krasnoselskii theorem.

Under the lack of the condition , some new convergence and stability theorems of Mann and Ishikawa iterative processes with errors for solutions to variational inclusions involving accretive mappings in real reflexive Banach spaces are established. The main results of this paper extend and improve the corresponding results obtained by Chang, Ding, Hassouni and Moudafi, Huang, Kazmi, Noor, Siddi...

In this paper we consider the convergence of iterative processes for a family of multivalued nonexpansive mappings. Under somewhat different conditions the sequences of Noor, Mann and Ishikawa iterates converge to the common fixed point of the family of multivalued nonexpansive mappings.

The purpose of this paper is to introduce a new class of quasi-contractive operators and to show that the most used fixed point iterative methods, that is, the Picard and Mann iterations, are convergent to the unique fixed point. The comparison of these methods with respect to their convergence rate is obtained.

In this paper, we introduce a modified Mann iterative process for strictly pseudo-contractive mappings and obtain a strong convergence theorem in the framework of q-uniformly smooth Banach spaces. Our results improve and extend the recent ones announced by (Kim and Xu 2005), (Xu 2004) and some others.

In this paper, we establish some fixed point theorems in connection with sequences of operators in the Banach space setting for Mann and Ishikawa iterative processes. Our results extend some of the results of Berinde, Bonsall, Nadler and Rus from complete metric space to the Banach space setting.

Piecewise Linear Representation has been widely used to compress online data which are collected by sensors. However, the current existing methods, including Piecewise Aggregate Approximation and Perceptually Important Points cannot own both advantages of calculation speed and recovery accuracy at the same time. In order to improve the Piecewise Linear Representation performance, this work prop...