• 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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1291-1297
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• 2014

In this paper, we investigate the value distribution of the difference operator on meromorphic functions, and obtain a difference analogue of a theorem of Hayman on meromorphic functions.

• 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.

• 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 = (𝕱_i). We also study some topological properties and prove some inclusion relations between these spaces.

• 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.

• 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.

• 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 ${\theta}$.

• 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.

• 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.

• 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.