Some new lacunary ff-statistical AA-convergent sequence spaces of order α\alpha

We study the concept of density for sets of natural numbers in some lacunary $A$-convergent sequence spaces. Also we are trying to investigate some relation between the ordinary convergence and module statistical convergence for evey unbounded modulus function. Morever we also study some results on the newly defined lacunary $f$-statistically $A$-convergent sequence spaces with respect to some Musielak-Orlicz function.Comment: Conference paper. arXiv admin note: text overlap with arXiv:1506.0545

A note on farthest point problem in Banach spaces

Farthest point problem states that "Must every uniquely remotal set in a Banach space be singleton?" In this paper we introduce the notion of partial ideal statistical continuity of a function which is way weaker than continuity of a function. We give an example to show that partial ideal statistical continuity is weaker than continuity. In this paper we use Ideal summability to give some answers to FPP problem which improves the result in [13]. We prove that if E is a non-empty, bounded, uniquely remotal subset in a real Banach space X such that E has a Chebyshev center c and the farthest point map F: X?E restricted to [c,F(c)] is partially ideal statistically continuous at c then E is singleton. ©2019 Miskolc University Press

An Orlicz Extension of Some New Sequence Spaces

The aim of this note is to introduce and study a new concept of lacunary σ-convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces

On P-convergence of four dimensional weighted sums of double random variables

The goal of this paper was to present a series of limit theorems that characterizes independent double random variables via four dimensional summability transformation. In order to accomplish this goal we began with the presentation of the following theorem that characterize pairwise independent random variables: let [xk,l] be a double sequence of pairwise independent random variables such that [xk, l] was uniformly integrable. Let [am, n, k, l] be a four dimensional matrix such that ≤ C for all ordered pair (m, n) and for some C and converges to 0 in probability Then (xk,l – E(xk,l) converges in mean to 0. Other extensions and variations via multidimensional transformation shall also be presented

On generalizations of certain summability methods using ideals

AbstractIn this paper, following the line of Savas and Das (2011) [10], we provide a new approach to two well-known summability methods by using ideals, introduce new notions, namely, I-statistical convergence and I-lacunary statistical convergence, investigate their relationship, and make some observations about these classes