• 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.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.597-610
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• 2016

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.291-298
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• 1998

The $L^p-L^q$ mapping properties of convolution operators with measures supported on curves in $\mathbb{R}^3$ have been studied by many authors. Oberlin provided examples of nondegenerate compact space curves whose arclength measures enjoy $L^p$-improving properties. This was later extended by Pan who showed that such properties hold for all nondegenerate compact space curves. In this paper, we will prove that the operator norm of the convolution operator with the arclength measure supported on a nondegenerate compact space curve depends only on certain quantities of the underlying curve.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.315-323
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• 2018

In this study, firstly we introduce generalized differential and integral operator, also using integral operator two classes are presented. Furthermore, some subordination results involving the Hadamard product (Convolution) for these subclasses of analytic function are proved. A number of consequences of some of these subordination results are also discussed.

• Proceedings of the Korea Information Processing Society Conference
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• 2017.11a
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• pp.799-802
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• 2017

We attempt to combines concepts of Morphological Operator(MO) and Convolutional Neural Networks(CNN) to improve image-to-image translation. To do this, we propose an operation that approximates morphological operations. Also we propose S-Convolution, an operation that extends the operation to use multiple filters like CNN. The experiment result shows that it can learn MO with big filter using multiple S-convolution layer of small filter. To validate effectiveness of the proposed layer in image-to-image translation we experiment with GAN with S-convolution applied. The result showed that GAN with S-convolution can achieve distinct result from that of GAN with CNN.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.599-619
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• 2005

We define the convolutions of Fourier hyperfunctions and show that every strongly decreasing Fourier hyperfunction is a convolutor for the space of Fourier hyperfunctions and the converse is true. Also we show that there are no differential operator with constant coefficients which have a fundamental solution in the space of strongly decreasing Fourier hyperfunctions. Lastly we show that the space of multipliers for the space of Fourier hyperfunctions consists of analytic functions extended to any strip in $\mathbb{C}^n$ which are estimated with a special exponential function exp$(\mu|\chi|)$.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.323-329
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• 2021

The main object of the present paper is to investigate some radius results of the functions f(z) = z + Σ^∞_n=2 a_nzⁿ(|z| < 1) with |a_n| ≤ n for all n ∈ ℕ. Some applications for certain operator defined through convolution are also considered.

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.191-214
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• 2018

The aim of this paper is to investigate the Fekete $Szeg{\ddot{o}}$ inequality for subclass of analytic functions defined by convolution between generalized Al-Oboudi differential operator and Srivastava-Attiya integral operator. Further, application to fractional derivatives are also given.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.259-275
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• 2007

The continuity for the multilinear operators associated to some non-convolution type integral operators on Besov spaces are obtained. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.567-574
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• 2022

We use convolution techniques to define certain classes of starlike functions which are associated with Lommel operator. Some inclusion results are investigated. It is also shown that these classes are invariant under Bernardi integral operator.