We introduce and study some basic properties of rough I- convergentpre-Cauchy sequences of triple sequence of Bernstein polynomials and also study the set of all rough I- limits of a pre-Cauchy sequence of triple sequence of Bernstein polynomials and relation between analytic ness and rough I- statistical convergence of pre-Cauchy sequence of a triple sequences of Bernstein polynomials .

In the paper, we investigate rough statistical approximation properties of (p; q)-analogue of Bernstein-Stancu Operators. We study approximation properties based on rough statistical convergence. We also study error bound using modulus of continuity.

This paper is to introduce the triple sequence spaces of intuitionistic rough I-convergent of BΛ3(μ,γ) (f, x, T ) and Bχ3(μ,γ) (f, x, T ) are defined by compact Bernstein operator and study the topology general properties.

We obtain a Korovkin-type approximation theorem for Bernstein Stancu polynomials of rough statistical convergence of triple sequences of positive linear operators of three variables from $H_{\omega}\left( K\right) $ to $C_{B}\left( K\right) $, where $K=[0,\infty)\times\lbrack0,\infty )\times\lbrack0,\infty)$ and $\omega$ is non-negative increasing function on $K$.

We introduce and study some basic properties of rough I-convergent of triple sequence of Bernstein polynomials and also study the set of all rough I-limits of a triple sequence of Bernstein polynomials and relation between analytic ness and rough I-statistical convergence of a triple sequences of Bernstein polynomials.

Abstract In this paper we define and study rough convergence of triple sequences and the set of rough limit points of a triple sequence. We also investigate the relations between the set of cluster points and the set of rough limit points of Cauchy sequences of triple sequence spaces.

The concept of partial metric space is a minimal generalization of a metric space (X, d), where for each x is an element of X, d(x, x) does not need to be zero, in other terms is known as non-self distance. In this conference paper we defined some new definitions on partial metric space using by first difference of a sequence (x(k)) in partial metric space and examined some properties of these definitions..

We study some connections between μ-lacunary strong χAuvw 3 convergence with respect to a mnk sequence of Musielak Orlicz function and μ-lacunary χAuvw 3 statistical convergence, where A is a sequence of four dimensional matrices A(uvw) = (ak1...krl1...ls 1r1s(uvw)) of complex numbers.

We introduce and study some basic properties of Bernstein-Stancu polynomials of rough I-convergent of triple sequence spaces and also study the set of all Bernstein-Stancu polynomials of rough I-limits of a triple sequence spaces and relation between analytic ness and Bernstein-Stancu polynomials of rough I-core of a triple sequence spaces.

Triple sequence convergence has an extremly important position in the basic theory of mathematics. The present manuscript contains four types of convergence concept of convergence almost surely, convergence incredibility, trust convergence in mean and convergence in distribution and discuss the relation ship among those and some mathematical properties of those new convergence.

The aim of this paper is to introduce multi rough and study a new concept of the χ2 space via ideal convergence of difference operator defined by Orlicz. Some topological properties of the resulting sequence spaces are also discussed.

The Bernstein operator is one of the important topics of approximation theory in which it has been studied in great details for a long time. The aim of this paper is to study the lambda-statistical convergence of sequence of Bernstein polynomials. In this paper, we introduce the concepts of lambda-statistical convergence of Bernstein polynomials and V(B)(lambda-)summability and related theorems.

In this paper, using the concept of natural density, we introduce the notion of Bernstein operator of rough statistical convergence of triple sequence. We define the set of Bernstein operator of rough statistical limit points of a triple sequence spaces and obtain Bernstein operator of statistical convergence criteria associated with this set. Later, we prove that this set is closed and convex and also examine the relations between the set of Bernstein operator of rough statistical cluster points and the set of Bernstein operator of rough statistical limit points of a triple sequences. C) 2017 The Authors. Published by IASE.

The main purpose of this paper is to introduce the spaces ?o? [A,M,?, p] and ?? [A,M,?,p] and ???[A,M,?,p] generated by infinite matrices defined by Orlicz functions. Some properties of these spaces are discussed. Also we introduce the concept of ?? [A,?]-statistical convergence and derive some results between the spaces ?? [A,?] and ??[A,?]. Further, we study some geometrical properties such as order continuous, the Fatou property and the Banach-Saks property of the new space ???? [A,?,p]. Finally, we introduce the notion of ??[A,?]-statistical convergence of order ? of real number sequences and obtain some inclusion relations between the set of ?[A,?]-statistical convergence of order ?.

In this paper we introduce the spaces V^λ[A,M,Δ,p]o,V^λ[A,M,Δ,p] and V^λ[A,M,Δ,p]∞ generated by infinite matrices defined by Orlicz functions. Also we introduce the concept of S^λ[A,Δ]−convergence and derive some results between the spaces S^λ[A,Δ] and V^λ[A,Δ]. Further, we study some geometrical properties such as order continuity, the Fatou property and the Banach–Saks property of the new space V^λα[A,Δ,p]∞. Finally, we introduce the notion of almost λ-statistically-[A, Δ]-convergence of order α or S^λα[A,Δ]−convergence and obtain some inclusion relations between the set S^λα[A,Δ] and the space V^λα[A,Δ,p]∞.

In this article, we introduce the sequence space m(M,A, φ, q) on generalizing the sequence space m(φ) which was defined by Sargent [8], defined by Orlicz functions and infinite matrices. We study its different properties like solidity, completeness, etc. Also we obtain some inclusion results involving the sequence space m(M,A, φ, q).