On difference sequence spaces of fractional-order involving Padovan numbers

2020 ◽  
pp. 2150095
Author(s):  
Taja Yaying ◽  
Bipan Hazarika ◽  
Syed Abdul Mohiuddine
Keyword(s):  
Fractional Order ◽  
Measure Of Noncompactness ◽  
Difference Operator ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Hausdorff Measure Of Noncompactness ◽  
Order Difference ◽  
Matrix Formula ◽  
Difference Sequence Spaces

In this paper, we introduce Padovan difference sequence spaces of fractional-order [Formula: see text] [Formula: see text] [Formula: see text] by the composition of the fractional-order difference operator [Formula: see text] and the Padovan matrix [Formula: see text] defined by [Formula: see text] and [Formula: see text] respectively, where the sequence [Formula: see text] is the Padovan sequence. We give some topological properties, Schauder basis and [Formula: see text]-, [Formula: see text]- and [Formula: see text]-duals of the newly defined spaces. We characterize certain matrix classes related to the [Formula: see text] space. Finally, we characterize certain classes of compact operators on [Formula: see text] using Hausdorff measure of noncompactness.

On generalized Fibonacci difference sequence spaces and compact operators

2021 ◽  
pp. 2250116
Author(s):  
Taja Yaying ◽  
Bipan Hazarika ◽  
Mikail Et
Keyword(s):  
Fractional Order ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Band Matrix ◽  
Matrix Formula ◽  
Necessary And Sufficient ◽  
Matrix Mappings ◽  
Difference Sequence Spaces

In this paper, we introduce Fibonacci backward difference operator [Formula: see text] of fractional order [Formula: see text] by the composition of Fibonacci band matrix [Formula: see text] and difference operator [Formula: see text] of fractional order [Formula: see text] defined by [Formula: see text] and introduce sequence spaces [Formula: see text] and [Formula: see text] We present some topological properties, obtain Schauder basis and determine [Formula: see text]-, [Formula: see text]- and [Formula: see text]-duals of the spaces [Formula: see text] and [Formula: see text] We characterize certain classes of matrix mappings from the spaces [Formula: see text] and [Formula: see text] to any of the space [Formula: see text] [Formula: see text] [Formula: see text] or [Formula: see text] Finally we compute necessary and sufficient conditions for a matrix operator to be compact on the spaces [Formula: see text] and [Formula: see text]

On sequence spaces generated by binomial difference operator of fractional order

2019 ◽  
Vol 69 (4) ◽  
pp. 901-918 ◽  
Author(s):  
Taja Yaying ◽  
Bipan Hazarika
Keyword(s):  
Fractional Order ◽  
Hausdorff Measure ◽  
Difference Operator ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Fractional Difference ◽  
Matrix Classes ◽  
The Matrix ◽  
Difference Sequence Spaces

Abstract In this article we introduce binomial difference sequence spaces of fractional order α, $\begin{array}{} b_p^{r,s} \end{array}$ (Δ(α)) (1 ≤ p ≤ ∞) by the composition of binomial matrix, Br,s and fractional difference operator Δ(α), defined by (Δ(α)x)k = $\begin{array}{} \displaystyle \sum\limits_{i=0}^{\infty}(-1)^i\frac{\Gamma(\alpha+1)}{i!\Gamma(\alpha-i+1)}x_{k-i} \end{array}$. We give some topological properties, obtain the Schauder basis and determine the α, β and γ-duals of the spaces. We characterize the matrix classes ( $\begin{array}{} b_p^{r,s} \end{array}$(Δ(α)), Y), where Y ∈ {ℓ∞, c, c0, ℓ1} and certain classes of compact operators on the space $\begin{array}{} b_p^{r,s} \end{array}$(Δ(α)) using Hausdorff measure of non-compactness. Finally, we give some geometric properties of the space $\begin{array}{} b_p^{r,s} \end{array}$(Δ(α)) (1 < p < ∞).

scholarly journals New Difference Sequence Spaces Defined by Musielak-Orlicz Function

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
M. Mursaleen ◽  
Sunil K. Sharma ◽  
S. A. Mohiuddine ◽  
A. Kılıçman
Keyword(s):  
Normed Space ◽  
Difference Operator ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

We introduce new sequence spaces by using Musielak-Orlicz function and a generalizedB∧ μ-difference operator onn-normed space. Some topological properties and inclusion relations are also examined.

scholarly journals On multiplicative difference sequence spaces and related dual properties

2017 ◽  
Vol 35 (3) ◽  
pp. 181-193 ◽  
Author(s):  
Ugur Kadak
Keyword(s):  
Present Article ◽  
Difference Operator ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Infinite Matrices ◽  
Dual Spaces ◽  
Difference Sequence Spaces

The main purpose of the present article is to introduce the multiplicative difference sequence spaces of order $m$  by defining the multiplicative difference operator $\Delta_{*}^m(x_k)=x^{}_k~x^{-m}_{k+1}~x^{\binom{m}{2}}_{k+2}~x^{-\binom{m}{3}}_{k+3}~x^{\binom{m}{4}}_{k+4}\dots x^{(-1)^m}_{k+m}$ for all $m, k \in \mathbb N$. By using the concept of multiplicative linearity various topological properties are investigated  and the relations related to their dual spaces are studied via multiplicative infinite matrices.

scholarly journals Measures of noncompactness in (N¯qΔ)summable difference sequence spaces

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5459-5470
Author(s):  
Ishfaq Malik ◽  
Tanweer Jalal
Keyword(s):  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Hausdorff Measure Of Noncompactness ◽  
Measures Of Noncompactness ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper we first introduce N?q?summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrices A to map these sequence spaces into the spaces c,c0, and l?. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces.

scholarly journals A note on multiordered fuzzy difference sequence spaces

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2867-2874
Author(s):  
Tanweer Jalal
Keyword(s):  
Difference Operator ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Difference Sequence ◽  
Topological Properties ◽  
Real Numbers ◽  
Ideal Convergence ◽  
Fuzzy Real Numbers ◽  
Difference Sequence Spaces

In this paper we introduce some new multi ordered difference operator on sequence spaces of fuzzy real numbers by using ideal convergence and modulus function and study their some algebraic and topological properties.

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