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In this paper, we propose a three-step iteration process and show that this process converges faster than a number of existing iteration processes. We give a numerical example followed by graphs to validate our claim. We prove strong and weak convergence results for approximating common fixed points for two nonexpansive mappings. Again we reconfirm our results by examples and tables. Further, we provide some applications of the our iteration process.

In this paper we propose a new three-step iteration process, called M iteration process, for approximation of fixed points. Some weak and strong convergence theorems are proved for Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Numerical example is given to show the efficiency of new iteration process. Our results are the extension, improvement and generalization of many known results in the literature of iterations in fixed point theory.

Let $H_1$, $H_2$, $H_3$ be real Hilbert spaces, let $A:H_1\rightarrow H_3$, $B:H_2\rightarrow H_3$ be two bounded linear operators. The general split common fixed-point problem under consideration in this paper is to $$\text{find}\ \ x \in \cap_{i=1}^p F(U_i),\ \ y \in \cap_{j=1}^r F(T_j)\ \ \text{such that}\ \ Ax = By,\eqno{(1)}$$ where $p$, $r\geq 1$ are integers, $U_i:H_1\rightarrow H_1$ $(1\leq i\leq p)$ and $T_j:H_2\rightarrow H_2$ $(1\leq j\leq r)$ are quasi-nonexpansive mappings with nonempty common fixed-point sets $\cap_{i=1}^pF(U_i)=\cap_{i=1}^p\{x\in H_1:U_ix=x\}$ and $\cap_{j=1}^rF(T_j)=\cap_{j=1}^r\{x\in H_2:T_jx=x\}$. Note that, the above problem (1) allows asymmetric and partial relations between the variables $x$ and $y$. If $H_2=H_3$ and $B=I$, then the general split common fixed-point problem (1) reduces to the general split common fixed-point problem proposed by Censor and Segal $\cite{C}$. In this paper, we introduce simultaneous parallel and cyclic algorithms for the general split common fixed-point problems (1). We introduce a way of selecting the stepsizes such that the implementation of our algorithms does not need any prior information about the operator norms. We prove the weak convergence of the proposed algorithms and apply the proposed algorithms to the multiple-set split feasibility problems. Our results improve and extend the corresponding results announced by many others.

In this work, we study convergence theorem, convergence rate and convergence speed of a new three-step iterative scheme for continuous functions on an arbitrary interval. We also give numerical examples for comparing with iterations of Mann, Ishikawa, Noor and Kadioglu-Yildirim.

We investigate the problem of ideal convergence of the sequences of linear operators without the properties of k-positivity in the space of analytic functions in a bounded simply connected domain of complex plane.

The purpose of this paper is to investigate variational inequalities, fixed point problems and generalized mixed equilibrium problems. Anextragradient iterative algorithm is investigated in the framework of Hilbert spaces. Weak convergence theorems for common solutions are established.

The notion of strong uniform convergence on bornologies introduced in 2009. by Beer-Levi turns to give the classical convergence introduced by Arzel? in 1883. Evert in 2003. introduced the notion of Arzel?-Whitney or simply AW-convergence for a net of functions. We define a new type of convergence, a "strong" form of Whitney convergence on bornologies, and we prove that on some families it coincides with that AW-convergence. Furthermore, we study the countability properties of this new function space.

Let K be a nonempty closed convex nonexpansive retract of a uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K ? E be non-self asymptotically nonexpansive in the intermediate sense mapping with F(T) = ?. Let {?ni}, {?ni} and {?ni} are sequences in [0, 1] with ?n(i) + ?n(i) + ?n(i) = 1 for all i = 1, 2, . . . , N. From arbitrary x1 ? K , define the sequence {xn } iteratively by (8), where {u(i) } for all i = 1, 2, . . . , N are bounded sequences in K with P? u(i) < ?. (i) If the dual E

Let (Xn) be a sequence of independent and non-identically distributed random variables. We assume that only observations of (Xn) at certain points are available. We study limit properties in the sense of weak convergence in the space D[0,1] of certain processes based on an incomplete sample from {X1, X2 ...,Xn }. This is an extension of the results of Matula and Stepien [2009. Weak convergence of products of sums of independent and non-identically distributed random variables. J. Math. Anal. Appl. 353, 49-54].

In a real Hilbert space H, starting from an arbitrary initial point x0 H, an iterative process is defined as follows: xn+1 = anxn +(1-an)T?n+1 f yn, yn = bnxn + (1 - bn)T?n g xn, n ? 0, where T ?n+1 f x = Tx - ?n+1?f f(Tx), T?n g x = Tx - ?n?gg(Tx), (8 x 2 H), T : H ? H a nonexpansive mapping with F(T) 6= ; and f (resp. g) : H ? H an ?f (resp. ?g)-strongly monotone and kf (resp. kg)-Lipschitzian mapping, {an} _ (0, 1), {bn} _ (0, 1) and {?n} _ [0, 1), {?n} _ [0, 1). Under some suitable conditions, several convergence results of the sequence {xn} are shown.

A notion of quasi-almost convergence, which is related to Banach limits, is defined and discussed.