• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.393-404
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• 2003

In general, a differential operator can be used as a tool of treating the local properties of given function. However, when the given function is varied with high frequency and has irregular form with non-stationary evolution it may not act its role sufficiently as in case of nowhere differentiable curves. In this paper we introduce a multi-scale derivative as a form of weakened global derivative so that it may explain its semi global diffusion properties as well as local ones for the various irregular diffusion phenomena.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.525-532
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• 2022

Let 𝓟_n denote the space of all complex polynomials $P(z)=\sum\limits_{j=0}^{n}{\alpha}_jz^j$ of degree n. Let P ∈ 𝓟_n, for any complex number α, D_αP(z) = nP(z) + (α - z)P'(z), denote the polar derivative of the polynomial P(z) with respect to α and B_n denote a family of operators that maps 𝓟_n into itself. In this paper, we combine the operators B and D_α and establish certain operator preserving inequalities concerning polynomials, from which a variety of interesting results can be obtained as special cases.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.21-36
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• 2024

In this paper, we study the existence of solutions for hybrid fractional differential equations with p-Laplacian operator involving fractional Caputo derivative of arbitrary order. This work can be seen as an extension of earlier research conducted on hybrid differential equations. Notably, the extension encompasses both the fractional aspect and the inclusion of the p-Laplacian operator. We build our analysis on a hybrid fixed point theorem originally established by Dhage. In addition, an example is provided to demonstrate the effectiveness of the main results.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.765-770
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• 2000

The object of the present paper is to give an application of a linear operator $L_p(a, c)$ defined by means of a Hadamard product (or convolution) to a Miller and Mocanu’s theorem.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.764-764
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• 2000

The object of the present paper is to give an application of a linear operator L(sub)p(a, c) defined by means of a Hadamard product (or convolution) to a Miller and Mocanu’s theorem.

• Journal of the Korea Society of Computer and Information
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• v.16 no.2
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• pp.61-69
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• 2011

Dynamic Time Warping based on Dynamic Programming is the one of the most widely been used to compare the similarity of two patterns. DTW algorithm has two known problems. The one is singularities. And the another problem is the accuracy of the warping path with patterns. Therefore, this paper suggest the solution for DTW algorithm to use a 2nd derivative operator. Laplacian of Gaussian is a kind of a 2nd derivative operator. Consequently, our suggestion method to apply to this operator, more efficient to solve the singularities problems and to secure a accuracy of the warping path. And the result shows a superior ability of this suggested method.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.473-482
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• 2015

Let Qf be the maximal derivative of f with respect to the Bergman metric $b_B$. In this paper, we will find conditions such that $(1-{\parallel}z{\parallel})^s(Qf)^p(z)$ is bounded on B. We will also find conditions such that Bergman projection type operator $P_r$ is bounded operator from $L^p(B,d{\mu}_r)$ to the holomorphic Besov p-space Bs $B^s_p(B)$ with weight s.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.427-444
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• 2011

In this paper we give some non-existence theorems for Hopf hypersurfaces in the complex two-plane Grassmannian $G_2(\mathbb{C}^{m+2})$ with Lie parallel normal Jacobi operator $\bar{R}_N$ and totally geodesic D and $D^{\bot}$ components of the Reeb flow.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1351-1370
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• 2018

In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order ${\alpha}$ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.