Generalized Statistically Almost Convergence Based on the Difference Operator which Includes the (p, q)-Gamma Function and Related Approximation Theorems
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DOI: 10.1007/s00025-018-0789-6
Abstract: This paper is devoted to extend the notion of almost convergence and its statistical forms with respect to the difference operator involving (p, q)-gamma function and an increasing sequence $$(\lambda _n)$$(λn) of positive numbers. We firstly… read more here.
Keywords: difference operator; almost convergence; gamma function; delta alpha ... See more keywords
The Structure of Fractional Spaces Generated by a Two-dimensional Difference Operator in a Half Plane
Sign Up to like & getrecommendations! Published in 2018 at "Ukrainian Mathematical Journal"
DOI: 10.1007/s11253-018-1561-5
Abstract: We consider a difference-operator approximation Ahx$$ {A}_h^x $$ of the differential operatorAxux=−a11xux1x1x−a22xux2x2x+σux,x=x1x2,$$ {A}^xu(x)=-{a}_{11}(x){u}_{x_1{x}_1}(x)-{a}_{22}(x){u}_{x_2{x}_2}(x)+\sigma u(x),\kern1em x=\left({x}_1,{x}_2\right), $$defined in the region ℝ+ × ℝ with the boundary condition u0x2=0,x2∈ℝ.$$ u\left(0,{x}_2\right)=0,\kern1em {x}_2\in \mathbb{R}. $$ Here, the coefficients aii(x),… read more here.
Keywords: difference; difference operator; spaces generated; structure fractional ... See more keywords
A note on q-difference operator and related limit direction
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DOI: 10.1016/s0252-9602(18)30839-7
Abstract: Abstract The growth of entire functions under the q-difference operators is studied in this paper, and then some properties of Julia set of entire functions under the higher order q-difference operators are obtained. read more here.
Keywords: difference; note difference; difference operator; operator related ... See more keywords
A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential
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DOI: 10.1155/2018/4696790
Abstract: The asymptotic and threshold behaviour of the eigenvalues of a perturbed difference operator inside a spectral gap is investigated. In particular, applications of the Titchmarsh-Weyl -function theory as well as the Birman-Schwinger principle is performed… read more here.
Keywords: threshold behaviour; inside spectral; asymptotic threshold; difference operator ... See more keywords
Quasi-Hadamard Product and Partial Sums for Sakaguchi-Type Function Classes Involving q-Difference Operator
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DOI: 10.3390/sym14040709
Abstract: We create two Sakaguchi-type function classes that are starlike and convex with respect to their symmetric points, including a q-difference operator, which may have symmetric or assymetric properties, in the open unit disc. We first… read more here.
Keywords: sakaguchi type; difference operator; type function; function classes ... See more keywords
Sequence Spaces and Spectrum of q-Difference Operator of Second Order
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DOI: 10.3390/sym14061155
Abstract: The sequence spaces ℓp(∇q2)(0≤p read more here.
Keywords: difference; operator second; sequence spaces; difference operator ... See more keywords
Symmetric Difference Operator in Quantum Calculus
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DOI: 10.3390/sym14071317
Abstract: The main focus of this paper is to develop certain types of fundamental theorems using q, q(α), and h difference operators. For several higher order difference equations, we get two forms of solutions: one is… read more here.
Keywords: difference equations; form; symmetric difference; difference operator ... See more keywords
On a Certain Subclass of p-Valent Analytic Functions Involving q-Difference Operator
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DOI: 10.3390/sym15010093
Abstract: This paper introduces and studies a new class of analytic p-valent functions in the open symmetric unit disc involving the Sălăgean-type q-difference operator. Furthermore, we present several interesting subordination results, coefficient inequalities, fractional q-calculus applications,… read more here.
Keywords: valent; subclass valent; certain subclass; difference operator ... See more keywords
Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications
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DOI: 10.7494/opmath.2021.41.4.489
Abstract: Let \(n\in\mathbb{N}^{*}\), and \(N\geq n\) be an integer. We study the spectrum of discrete linear \(2n\)-th order eigenvalue problems \[\begin{cases}\sum_{k=0}^{n}(-1)^{k}\Delta^{2k}u(t-k) = \lambda u(t) ,\quad & t\in[1, N]_{\mathbb{Z}}, \\ \Delta^{i}u(-(n-1))=\Delta^{i}u(N-(n-1)),\quad & i\in[0, 2n-1]_{\mathbb{Z}},\end{cases}\] where \(\lambda\) is… read more here.
Keywords: difference operator; order; spectrum discrete; order difference ... See more keywords