The purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive operators in a strictly convex Banach spacehaving a uniformly Gateaux differentiable norm. As a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

In this work we use the Noor iteration process for total asymptotically nonexpansive mapping to establish the strong and $Delta$-convergence theorems in the framework of CAT(0) spaces. By doing this, some of the results existing in the current literature  generalize, unify and extend.

We discuss in this paper the strong convergence for weighted sums of negatively orthant dependent (NOD) random variables by generalized Gaussian techniques. As a corollary, a Cesaro law of large numbers of i.i.d. random variables is extended in NOD setting by generalized Gaussian techniques.

Support vector data description (SVDD) is a useful method for outlier detection and has been applied to a variety of applications. However, in the existing optimization procedure of SVDD, there are some issues which may lead to improper usage of SVDD. Some of the issues might already be known in practice, but the theoretical discussion, justification and correction are still lacking. Given the ...

Let (Ω,F ,P) be a probability space, and let {Xn} be a sequence of integrable centered i.i.d. random variables. In this paper we consider what conditions should be imposed on a complex sequence {bn} with |bn| → ∞, in order to obtain a.s. convergence of P n Xn bn , whenever X1 is in a certain class of integrability. In particular, our condition allows us to generalize the rate obtained by Marcin...

The problem of Shannon entropy estimation in countable infinite alphabets is revisited from the adoption of convergence results of the entropy functional. Sufficient conditions for the convergence of the entropy are used, including scenarios with both finitely and infinitely supported distributions. From this angle, four plug-in histogram-based estimators are studied showing strong consistency ...

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 regular asymptotically 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

The Fréchet mean or barycenter generalizes the idea of averaging in spaces where pairwise addition is not well-defined. In general metric spaces, the Fréchet sample mean is not a consistent estimator of the theoretical Fréchet mean. For graph-valued random variables, for instance, the Fréchet sample mean may fail to converge to a unique value. Hence, it becomes necessary to consider the converg...

Abstract: We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in R. Our study covers both the case where the true underlying density is log-concave, and where this model is misspecified. We begin by showing that for a sequence of log-concave densities, convergence in distribution implies much s...