We study the convergence of Ishikawa iteration process for the class of asymptotically κ-strict pseudocontractive mappings in the intermediate sense which is not necessarily Lipschitzian. Weak convergence theorem is established. We also obtain a strong convergence theorem by using hybrid projection for this iteration process. Our results improve and extend the corresponding results announced by...

After introducing many different types of prefilter convergence, we introduce an universal method to define various notions of compactness using cluster point and convergence of a prefilter and to prove the Tychonoff theorem using characterizations of ultra(maximal) prefilters. : prefilter convergence, universal method, Tychonoff theorem, ultra prefilter, good extension

In this paper, we first obtain a weak mean convergence theorem of Baillon’s type for generalized hybrid mappings in a Hilbert space. Further, using an idea of mean convergence, we prove a strong convergence theorem of Halpern’s type for generalized hybrid mappings in a Hilbert space.

It is proved that generalized excursion measures can be constructed via time change of Itô’s Brownian excursion measure. A tightness-like condition on strings is introduced to prove a convergence theorem of generalized excursion measures. The convergence theorem is applied to obtain a conditional limit theorem, a kind of invariance principle where the limit is the Bessel meander.

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...

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...

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...

BGP allows routers to use general preference policies for route selection. This paper studies the impact of these policies on convergence time. We first describe a real-time model of BGP. We then state and prove a general theorem providing an upper bound on convergence time. Finally, we show how to the use the theorem to prove convergence and estimate convergence time in three case studies.