• Title/Summary/Keyword: difference operator

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DISTRIBUTION OF VALUES OF DIFFERENCE OPERATORS CONCERNING WEAKLY WEIGHTED SHARING

  • SHAW, ABHIJIT
    • Journal of applied mathematics & informatics
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    • v.40 no.3_4
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    • pp.545-562
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    • 2022
  • Using the conception of weakly weighted sharing we discussed the value distribution of the differential product functions constructed with a polynomial and difference operator of entire function. Here we established two uniqueness result on product of difference operators when two such functions share a small function.

ON THE FINITE DIFFERENCE OPERATOR $l_{N^2}$(u, v)

  • Woo, Gyung-Soo;Lee, Mi-Na;Seo, Tae-Young
    • East Asian mathematical journal
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    • v.16 no.1
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    • pp.97-103
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    • 2000
  • In this work, we consider a finite difference operator $L^2_N$ corresponding to $$Lu:=-(u_{xx}+u_{yy})\;in\;{\Omega},\;u=0\;on\;{\partial}{\Omega}$$, in $S_{h^2,1}$. We derive the relation between the absolute value of the bilinear form $l_{N^2}$(u, v) on $S_{h^2,1}{\times}S_{h^2,1}$ and Sobolev $H^1$ norms.

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SOME SEQUENCE SPACES OVER n-NORMED SPACES DEFINED BY FRACTIONAL DIFFERENCE OPERATOR AND MUSIELAK-ORLICZ FUNCTION

  • Mursaleen, M.;Sharma, Sunil K.;Qamaruddin, Qamaruddin
    • Korean Journal of Mathematics
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    • v.29 no.2
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    • pp.211-225
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    • 2021
  • In the present paper we introduce some sequence spaces over n-normed spaces defined by fractional difference operator and Musielak-Orlicz function 𝓜 = (𝕱i). We also study some topological properties and prove some inclusion relations between these spaces.

ON p, q-DIFFERENCE OPERATOR

  • Corcino, Roberto B.;Montero, Charles B.
    • Journal of the Korean Mathematical Society
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    • v.49 no.3
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    • pp.537-547
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    • 2012
  • In this paper, we define a $p$, $q$-difference operator and obtain an explicit formula which is used to express the $p$, $q$-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the $p$, $q$-difference operator. Explicit formulas for the non-central $q$-Stirling numbers of the second kind and non-central $q$-Lah numbers are derived using the new $q$-analogue of Newton's interpolation formula. Moreover, a $p$, $q$-analogue of Newton's interpolation formula is established.

Stability Criterion for Volterra Type Delay Difference Equations Including a Generalized Difference Operator

  • Gevgesoglu, Murat;Bolat, Yasar
    • Kyungpook Mathematical Journal
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    • v.60 no.1
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    • pp.163-175
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    • 2020
  • The stability of a class of Volterra-type difference equations that include a generalized difference operator ∆a is investigated using Krasnoselskii's fixed point theorem and some results are obtained. In addition, some examples are given to illustrate our theoretical results.

STABILITY OF HAHN DIFFERENCE EQUATIONS IN BANACH ALGEBRAS

  • Abdelkhaliq, Marwa M.;Hamza, Alaa E.
    • Communications of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1141-1158
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    • 2018
  • Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

Comparative Analysis of Spectral Theory of Second Order Difference and Differential Operators with Unbounded Odd Coefficient

  • Nyamwala, Fredrick Oluoch;Ambogo, David Otieno;Ngala, Joyce Mukhwana
    • Kyungpook Mathematical Journal
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    • v.60 no.2
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    • pp.297-305
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    • 2020
  • We show that selfadjoint operator extensions of minimal second order difference operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.

CONVOLUTION PROPERTIES FOR ANALYTIC FUNCTIONS DEFINED BY q-DIFFERENCE OPERATOR

  • Cetinkaya, Asena;Sen, Arzu Yemisci;Polatoglu, Yasar
    • Honam Mathematical Journal
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    • v.40 no.4
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    • pp.681-689
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    • 2018
  • In this paper, we defined new subclasses of Spirallike and Robertson functions by using concept of q-derivative operator. We investigate convolution properties and coefficient estimates for both classes q-Spirallike and q-Robertson functions denoted by ${\mathcal{S}}^{\lambda}_q[A,\;B]$ and ${\mathcal{C}}^{\lambda}_q[A,\;B]$, respectively.

A DIFFERENCE EQUATION FOR MULTIPLE KRAVCHUK POLYNOMIALS

  • Lee, Dong-Won
    • Journal of the Korean Mathematical Society
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    • v.44 no.6
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    • pp.1429-1440
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    • 2007
  • Let ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ be a multiple Kravchuk polynomial with respect to r discrete Kravchuk weights. We first find a lowering operator for multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ in which the orthogonalizing weights are not involved. Combining the lowering operator and the raising operator by Rodrigues# formula, we find a (r+1)-th order difference equation which has the multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ as solutions. Lastly we give an explicit difference equation for ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ for the case of r=2.