Within the last decade, there has been growing interest in the study of multiple solutions of twoand multi-point boundary value problems of nonlinear ordinary differential equations as fixed points of a cone mapping. Undeniably many good results have emerged. The purpose of this paper is to point out that, in the special case of second-order equations, the shooting method can be an effective to...

The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made. The argument involves theory for a new class of weighted and marked empirical processes, quantile ...

In this paper, motivated by Khan et. al.[11], we use three-step iterative procedures with errors to approximate fixed point of multivalued quasinonexpansive mappings in uniformly Banach space and establish strong and weak convergence theorems for the proposed process. Our results extend important results. Mathematics Subject Classification: Primary 47H10; Secondary 47J25

Let C be a nonempty closed convex subset of a smooth Banach space E and let A be an accretive operator of C into E. We first introduce the problem of finding a point u ∈ C such that 〈Au, J(v− u)〉 ≥ 0 for all v ∈ C, where J is the duality mapping of E. Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol’shteı̆n and Tret’yakov i...

The purpose of this paper is to introduce a new iterative algorithm for a semigroup of nonexpansive operators in Hilbert space. We prove that the proposed iterative algorithm converges strongly to the minimum-norm common fixed point of the semigroup of nonexpansive operators. The results of this paper extend and improve some known results in the literature. AMS subject classifications: 41A65, 4...

In this work, we analyze the discrete in time 3D system for the globally modified Navier–Stokes equations introduced by Caraballo (2006) [1]. More precisely, we consider the backward implicit Euler scheme, and prove the existence of a sequence of solutions of the resulting equations by implementing the Galerkin method combined with Brouwer’s fixed point approach. Moreover, with the aid of discr...

The purpose of this paper is to establish a strong convergence of an explicit iteration scheme with mean errors to a common fixed point for a finite family of Ćirić quasi-contractive operators in normed spaces. The results presented in this paper generalize and improve the corresponding results of V.Berinde [1], A.Rafiq [9], B. E. Rhoades [10] and T. Zamfirescu [12].

Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand Abstract In this article, we introduce a new mapping generated by infinite family of nonexpansive mapping and infinite real numbers. By means of the new mapping, we prove a strong convergence theorem for finding a common element of the se...

In real Hilbert spaceH , from an arbitrary initial point x0 ∈H , an explicit iteration scheme is defined as follows: xn+1 = αnxn + (1 − αn)Tn+1xn,n ≥ 0, where Tn+1xn = Txn − λn+1μF(Txn), T :H →H is a nonexpansive mapping such that F(T) = {x ∈ K : Tx = x} is nonempty, F :H →H is a η-strongly monotone and k-Lipschitzian mapping, {αn} ⊂ (0,1), and {λn} ⊂ [0,1). Under some suitable conditions, the ...

Recently, in [5], Najati and Moradlou proved Hyers-Ulam-Rassias stability of the following quadratic mapping of Apollonius type Q(z − x) + Q(z − y) = 1 2 Q(x− y) + 2Q ( z − x + y 2 ) in non-Archimedean space. In this paper we establish Hyers-Ulam-Rassias stability of this functional equation in random normed spaces by direct method and fixed point method. The concept of Hyers-Ulam-Rassias stabi...