arXiv subjects

Taja Yaying

Publications and source records attributed to Taja Yaying.

5 recordsLinked to original sources

arXiv2025

Some q-fractional order difference sequence spaces

This paper intends to develop a $q$-difference operator $\nabla^{(\gamma)}_q$ of fractional order $\gamma$, and give several intriguing properties of this new difference operator. Our main focus remains on the construction of sequence spaces $\ell_p(\nabla^{(\gamma)})$ and $\ell_\infty (\nabla^{(\gamma)})$, at the same time comparing these spaces with those already exist in the literature. Apart from obtaining Schauder basis, we determine $\alpha$-, $\beta$-, and $\gamma$-duals of the newly defined spaces. A section is also devoted for characterizing matrix classes $(\ell_p(\nabla^{(\gamma)}),\mathfrak X),$ where $\mathfrak X$ is any of the spaces $\ell_\infty,$ $c,$ $c_0$ and $\ell_1$.

math.FA↗

arXiv2024

On the Double Sequence Space $\mathcal{H}_{\vartheta}$ as an Extension of Hahn Space $h$

Double sequence spaces have become a significant area of research within functional analysis due to their applications in various branches of mathematics and mathematical physics. In this study, we investigate Hahn double sequence space denoted as $\mathcal{H}_{\vartheta}$, where $\vartheta\in\{p,bp,r\}$, as an extension of the Hahn sequence space $h$. Our investigation begins with an analysis of several topological properties of $\mathcal{H}_{\vartheta}$, apart from a comprehensive analysis of the relationship between Hahn double sequences and some other classical double sequence spaces. The $α-$dual, algebraic dual and $β(bp)-$dual, and $γ-$dual of the space $\mathcal{H}_{\vartheta}$ are detrmined. Furthermore, we define the determining set of $\mathcal{H}_{\vartheta}$ and we state the conditions concerning the characterization of four-dimensional (4D) matrix classes $(\mathcal{H}_{\vartheta},λ)$, where $λ=\{\mathcal{H}_{\vartheta},\mathcal{BV}, \mathcal{BV}_{\vartheta 0}, \mathcal{CS}_{\vartheta},\mathcal{CS}_{\vartheta 0},\mathcal{BS}\}$ and $(μ,\mathcal{H}_{\vartheta})$, where $μ=\{\mathcal{L}_u, \mathcal{C}_{\vartheta 0}, \mathcal{C}_{\vartheta},\mathcal{M}_{u}\}$. In conclusion, this research contributes non-standard investigation and various significant results into the space $\mathcal{H}_{\vartheta}$. The conducted results are deepen the understanding of the space $\mathcal{H}_{\vartheta}$ and open up new avenues for further research and applications in sequence space theory.

math.FA↗

arXiv2018

Arithmetic summable sequence space over non-Newtonian field

Recently Ruckle \cite{RuckleArithmeticalSummability} introduced the theory of arithmetical summability suggested by the sum $ \sum_{k|m}f(k) $ as $ k $ ranges over the divisors of $m$ including $ 1 $ and $ m .$ Following Ruckle \cite{RuckleArithmeticalSummability} we construct the sequence space $ AS(G) $ and $ AC(G) $ of arithmetic summable and arithmetic convergent sequences in the sense of geometric calculus and derive interesting results in the geometric field.

math.GM↗

arXiv2017

Lacunary arithmetic statistical convergence

A lacunary sequence is an increasing integer sequence $θ=(k_r)$ such that $k_r-k_{r-1}\rightarrow \infty$ as $r\rightarrow \infty.$ In this article we introduce arithmetic statistically convergent sequence space $ASC$ and lacunary arithmetic statistically convergent sequence space $ASC_θ$ and study some inclusion properties between the two spaces. Finally we introduce lacunary arithmetic statistical continuity and establish some interesting results.

math.GM↗

arXiv2016

Lacunary Arithmetic convergence

In this article we introduce and study the lacunary arithmetic convergent sequence space $AC_θ$. Using the idea of strong Cesàro summable sequence and arithmetic convergence we define $AC_{σ_1}$ and study the relations between $AC_θ$ and $AC_{σ_1}$. Finally using modulus function we define $AC_θ(f)$ and study some interesting results.

math.FA↗