Related papers: Lacunary statistical convergence of order beta in …
In this paper, we extend the notions of statistically convergence of order $\beta $ and strong Ces\`{a}ro summability of order $\beta ,$ and introduce the notions $f-$statistically convergence of order $\beta $ and strong Ces\`{a}ro…
Let $\Delta^{(\alpha)}$ denote the fractional difference operator. In this paper, we define new difference sequence spaces $c_0(\Gamma,\Delta^{(\alpha)},u)$ and $c(\Gamma,\Delta^{(\alpha)},u)$. Also, the $\beta-$ dual of the spaces…
The main purpose of this paper is to introduce lacunary strong geometric zweier convergent sequence spaces $N_{\theta }^{0} \left[Z\left(G\right)\right]$, $N_{\theta } \left[Z\left(G\right)\right]$, $N_{\theta }^{\infty }…
This paper studies the linear stochastic partial differential equation of fractional orders both in time and space variables $\left(\partial^\beta + \frac{\nu}{2} (-\Delta)^{\alpha/2} \right) u(t,x)= \lambda u(t,x) \dot{W}(t,x)$, where…
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…
In the present paper, by using the band matrix F defined by the Fibonacci sequence, we introduce the sequence sequence spaces c_0(F) and c(F). Also, we give some inclusion relations and construct the bases of the spaces c_0(F) and c(F).…
In this paper, new sequence spaces $X(r, s, t ;\Delta^{(m)})$ for $X\in \{l_\infty, c, c_0\}$ defined by using generalized means and difference operator of order $m$ are introduced. It is shown that these spaces are complete normed linear…
In this article we introduce and study the lacunary arithmetic convergent sequence space $AC_{\theta}$. Using the idea of strong Ces\`{a}ro summable sequence and arithmetic convergence we define $AC_{\sigma_1}$ and study the relations…
Based on the concept of new type of statistical convergence defined by Aktuglu, we have introduced the weighted $\alpha\beta$ - statistical convergence of order $\theta$ in case of fuzzy functions and classified it into pointwise, uniform…
We have introduced a new sequence space $l(r, s, t, p ;\Delta^{(m)})$ combining by using generalized means and difference operator of order $m$. We have shown that the space $l(r, s, t, p ;\Delta^{(m)})$ is complete under some suitable…
In this study, we define the spaces $\mathcal{M}_{u}(\Delta),\mathcal{C}_{p}(\Delta),\mathcal{C}_{0p}(\Delta), \mathcal{C}_{r}(\Delta)$ and $\mathcal{L}_{q}(\Delta)$ of double sequences whose difference transforms are bounded , convergent…
This paper deals with new sequence spaces $X(r, s, t ;\Delta) $ for $X\in \{l_\infty, c, c_0\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete normed linear spaces and the spaces $X(r,…
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…
We determine the structure of the set of intermediate $\beta$-shifts of finite type. Specifically, we show that this set is dense in the parameter space $\Delta = \{ (\beta, \alpha) \in \mathbb{R}^{2} \colon \beta \in (1, 2) \; \text{and}…
In this paper, we investigate a class of fractional Hardy type operators $\mathscr{H}_{\beta_{1},\cdots,\beta_{m}}$ defined on higher-dimensional product spaces…
The concept of weighted $\beta\gamma$ - summability of order $\theta$ in case of fuzzy functions is introduced and classified into ordinary and absolute sense. Several inclusion relations among the sets are investigated. Also we have found…
The main purpose of this article is to introduce Pascal difference sequence spaces of fractional order $ \tau $ over the sequence space $\ell_p$ and $\ell_\infty$. Some topological properties of these spaces are considered here along with…
The reduction modulo $p$ of a family of lacunary integer polynomials, associated with the dynamical zeta function $\zeta_{\beta}(z)$ of the $\beta$-shift, for $\beta > 1$ close to one, is investigated. We briefly recall how this family is…
In this paper, we introduce some new double sequence spaces $\mathcal{M}_u(\Delta)$ and $\mathcal{C}_{\vartheta}(\Delta)$, where $\vartheta\in\{bp,bp0,r,r0\}$ as the domains of the four-dimensional forward difference matrix in the double…
The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$ We also establish a few inclusion relations concerning this space and determine…