we introduce a new one-step iteration process to approximate common fixed points of twononexpansive mappings in banach spaces and prove weak convergence of the iterative sequence using (i)opial’s condition and (ii) kadec-klee property. strong convergence theorems are also established in banachspaces and uniformly convex banach spaces under the so-called condition ( a ), which is weaker thancom...

in this paper, we will present a modification of the preconditioned aor-type method for solving the linear system. a theorem is given to show the convergence rate of modification of the preconditioned aor methods that can be enlarged than the convergence aor method.

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}

We study classes of filters F on N such that weak and strong F -convergence of sequences in l1 coincide. We study also analogue of l1 weak sequential completeness theorem for filter convergence.

Convergence under various topologies and analytical properties of power series on Levi-Civita fields are studied. A radius of convergence is established that asserts convergence under a weak topology and reduces to the conventional radius of convergence for real power series. It also asserts strong (order) convergence for points the distance of which from the center is infinitely smaller than t...

recently, mohiuddine and alghamdi introduced the notion of lacunary statistical convergence in a locally solid riesz space and established some results related to this concept. in this paper, some inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences are established and extensions of a decomposition theorem, a tauberian theorem to the l...

We prove that if a set is ‘large’ in the sense of Erdős, then it approximates arbitrarily long arithmetic progressions strong quantitative sense. More specifically, expressing error approximation terms gap length $\Delta$ progression, we improve previous result $o(\Delta)$ to $O(\Delta^\alpha)$ for any $\alpha \in (0,1)$. This improvement comes from new approach relying on an iterative applicat...

We treat a quantum walk (QW) on the line whose quantum coin at each vertex tends to be the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a “power-law” decay around the origin and a “strongly” ballistic spreading called bottom localization in this paper. This limit theorem implies the weak convergence with line...

In this paper, the homotopy analysis method (HAM) is considered to obtain the solution of the Schrodinger equation with a power law nonlinearity. For this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. Also, an example is solved to illustrate the eciency of the mentioned algorithm and the h-curve is plotted to determine the region ...