Digital Object Identifier: 10.1109/ TNN.2009.2025946 “Convergence analysis of the online BP training algorithm was proved using two fundamental theorems: One theorem claims that under mild conditions, the gradient sequence of the error function will converge to zero (the weak convergence), and another theorem concludes the convergence of the weight sequence defined by the procedure to a fixed v...

In this paper, we deal with the problem of finding a common fixed point of a family of relatively nonexpansive mappings. We, first of all, discuss the properties of strongly relatively nonexpansive mappings and show a strong convergence theorem for a sequence of relatively nonexpansive mappings under some conditions. Using this result, we obtain a strong convergence theorem for a finite family ...

The purpose of this paper is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-φ-nonexpansive mappings. The strong convergence theorem is proven in the more general reflexive, strictly convex, and smooth Banach spaces with the property K . The results of this paper improve and extend the results of S. Matsushita and W. Takahashi 2005 ...

Suppose K is a closed convex subset of a real reflexive Banach space E which has a uniformly Gâteaux differentiable norm and every nonempty closed convex bounded subset of E has the fixed point property for nonexpansive mappings. We prove a strong convergence theorem for an m−accretive mapping from K to E. The results in this paper are different from the corresponding results in [8] and they im...

‎Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove a strong convergence theorem for approximating a solution of split equality fixed point problem for quasi-nonexpansive mappings in a real Hilbert space‎. ‎So many have used algorithms involving the operator norm for solving split equality fixed point problem‎, ‎...

We introduce an explicit iterative scheme for computing a common fixed point of a sequence of nearly nonexpansive mappings defined on a closed convex subset of a real Hilbert space which is also a solution of a variational inequality problem. We prove a strong convergence theorem for a sequence generated by the considered iterative scheme under suitable conditions. Our strong convergence theore...

Every one of the important strong limit theorems that we have seen thus far – the strong law of large numbers, the martingale convergence theorem, and the ergodic theorem – has relied in a crucial way on a maximal inequality. This is no accident: it can in fact be shown that a maximal inequality is a necessary condition for an almost everywhere convergence theorem. We will refrain from carrying...

We introduce the hybrid method of modified Mann’s iteration for an asymptotically k-strict pseudo-contractive mapping T in the intermediate sense which is necessarily lipschitzian. We establish strong convergence theorem for such method. The result extend and improve the recent ones announced by Inchan and Nammanee, Inchan and concern result of Takahashi, Takeuchi and Kubota [Strong convergence...