Search

In this paper we study the domain of generalized Riesz difference matrix RqΔ(α) of fractional order α in the classical sequence spaces c0 and c and introduced the sequence spaces r 0 q (Δ (α)) and r c q (Δ (α)). We obtain the α−, β− and γ−duals of these spaces and using Hausdorff measure of noncompactness, we characterize certain classes of compact operators on the space r 0 q (Δ (α)). [ABSTRACT FROM AUTHOR]

In this paper we introduce and study some properties of the new sequence space of order α which is defined using the modulus and ϕ function. Furthermore some connections between V μ α ((T , φ)) - strong summability of sequences and μ− strong convergence of order α with respect to a modulus are studied. [ABSTRACT FROM AUTHOR]

The concept of P-convergent double sequence spaces was presented in 1988 by Moricz and Rhoades, and also in 2005, the notion of almost lacunary strongly P-convergent double sequences was introduced by Savas and Patterson, using Orlicz functions. Following these two concepts, we present the double almost lacunary strongly P-convergent of weight g via Orlicz functions in 2-Normed spaces. Additionally, inclusion theorems and extension of existing results in the literature will be established. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the concept of Abel statistical delta ward compactness and Abel statistical delta ward continuity in metric spaces. A function f defined on a metric space X into X is called Abel statistically delta ward continuous it preserves Abel statistical delta quasi Cauchy sequences, where a sequence (xk) of points in X is called Abel statistically delta quasi Cauchy if lim x → 1 − (1 − x) ∑ k : | d (x k + 2 , x k + 1 − d (x k + 1 , x k ) | ≥ ε x k = 0 for every ε > 0, Some other types of compactnesses are also studied and interesting results are obtained. [ABSTRACT FROM AUTHOR]

In this extended abstract, we introduce the concept of delta quasi Cauchy sequences in metric spaces. A function f defined on a subset of a metric space X to X is called delta ward continuous if it preserves delta quasi Cauchy sequences, where a sequence (xk) of points in X is called delta quasi Cauchy if lim n → ∞ [ d (x k + 2 , x k + 1) − d (x k + 1 , x k) ] = 0. A new type compactness in terms of δ-quasi Cauchy sequences, namely δ-ward compactness is also introduced, and some theorems related to δ-ward continuity and δ-ward compactness are obtained. Some other types of continuities are also discussed, and interesting results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate ideal strong lacunary ward continuity in 2-normed spaces. A function f on a subset A of a 2-normed space X into X is ideal strongly lacunary ward continuous if it preserves ideal strong lacunary quasi-Cauchy sequences of points in A. We also studied some other kinds of continuities. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study characterization of strongly λ- invariant regular matrices, uniqueness of generalized limits and inclusion relations of such sequences have been discussed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the concept of Abel statistical ward continuity in 2-normed spaces. A function f defined on a 2-normed space X into X is called Abel statistically ward continuous if it preserves Abel statistical quasi Cauchy sequences, where a sequence (xk) of points in X is called Abel statistically quasi Cauchy if lim x → 1 − (1 − x) ∑ k : | | Δ x k , z | | ≥ ε x k = 0 for every ε > 0 and z ∈ X, where Δxk = xk+1 − xk for every k ∈ N. Some other types of compactness and continuities are also studied and interesting results are obtained. [ABSTRACT FROM AUTHOR]