A stochastic iterative algorithm approximating second-order information using von Neumann series is discussed. We present convergence guarantees for stronglyconvex and smooth functions. Our analysis is much simpler in contrast to a similar algorithm and its analysis, LISSA. The algorithm is primarily suitable for training large scale linear models, where the number of data points is very large....

We establish strong convergence result of split feasibility problem for a family of quasi-nonexpansive multi-valued mappings and a total asymptotically strict pseudo-contractive mapping in infinite dimensional Hilbert spaces. Acknowledgement. The authors A. R. Khan and M. Abbas are grateful to King Fahd University of Petroleum and Minerals for supporting research project IN 121037.

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...

in this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regularasymptotically nonexpansive mappings in a real reflexive banach space with a uniformly g$hat{a}$teaux differentiable norm. our result is applicable in $l_{p}(ell_{p})$ spaces,$1 < p

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

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 characterize all geometric perturbations of an open set, for which the solution of a nonlinear elliptic PDE of p-Laplacian type with Dirichlet boundary condition is stable in the L∞-norm. The necessary and sufficient conditions are jointly expressed by a geometric property associated to the γp-convergence. If the dimension of the space N satisfies N − 1 < p ≤ N and if the number of the conne...

We give estimates of the distance between the densities of the laws of two functionals F and G on the Wiener space in terms of the Malliavin-Sobolev norm of F −G. We actually consider a more general framework which allows one to treat with similar (Malliavin type) methods functionals of a Poisson point measure (solutions of jump type stochastic equations). We use the above estimates in order to...