• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.125-136
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• 2020

In this article, we discuss classes of generalized functions for certain modified integral operator of Bessel-type involving Fox's H-function kernel. We employ a known differentiation formula of Fox's H-function to obtain the definition and properties of the distributional modified Bessel-type integral. Further, we derive a smoothness theorem for its kernel in a complete countably multi-normed space. On the other hand, using an appropriate class of convolution products, we derive axioms and establish spaces of modified Boehmians which are generalized distributions. On the defined spaces, we introduce addition, convolution, differentiation and scalar multiplication and further properties of the extended integral.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.193-207
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• 1999

Let ${\gamma}$ : Ilongrightarrow R2 be a sufficiently smooth curve and $\sigma$${\gamma}$ be the affine arclength measure supported on ${\gamma}$. In this paper, we study the Lp - improving properties of the convolution operators T$\sigma$${\gamma}$ associated with $\sigma$${\gamma}$ for various curves ${\gamma}$. Optimal results are obtained for all finite type plane curves and homogeneous curves (possibly blowing up at the origin). As an attempt to extend this result to infinitely flat curves we give and example of a family of flat curves whose affine arclength measure has same Lp-improvement property. All of these results will be based on uniform estimates of damping oscillatory integrals.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.301-314
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• 2019

The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. For these functions, for linear combinations of these functions and their derivatives, for operators defined by convolution products, and for the Alexander-type integral operator, we find simple sufficient conditions such that these mapping belong to a general class of functions defined and studied by Goodman, Rønning, and Bharati et al.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.377-389
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• 2020

In this paper, we are mainly interested to find sufficient conditions for the convolution operator 𝓨_λ,µf(z) = zW_λ,µ(z) ∗ f(z) belonging to the classes 𝓤𝓒𝓥 (k, α), 𝓢_p (k, α), S*_ς and C_ς.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.843-854
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• 2020

The purpose of this present paper is to obtain inclusion relations between various subclasses of harmonic univalent functions by using the convolution operator associated with generalized distribution series. To be more precise, we obtain such inclusions with harmonic starlike and harmonic convex mappings in the plane.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.529-538
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• 2018

The purpose of the present paper is to establish connections between various subclasses of analytic univalent functions by applying certain convolution operator involving Poisson distribution series. To be more precise,we investigate such connections with the classes of analytic univalent functions with positive coefficients in the open unit disk.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.467-478
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• 2013

The purpose of the present paper is to establish some interesting results involving coefficient conditions, extreme points, distortion bounds and covering theorems for the classes $V_H({\beta})$ and $U_H({\beta})$. Further, various inclusion relations are also obtained for these classes. We also discuss a class preserving integral operator and show that these classes are closed under convolution and convex combinations.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.701-717
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• 2020

We introduced and studied a new class of harmonic univalent functions on unit disc 𝕌. Also we provided coefficient conditions, extreme points and convolution conditions for that class of harmonic univalent functions.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.119-142
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• 2021

In this paper, we first introduce a new L_p analytic Fourier-Feynman transform with respect to subordinate Brownian motion (AFFTSB), which extends the Fourier-Feynman transform in the Wiener space. We next examine several relationships involving the L_p-AFFTSB, the convolution product, and the gradient operator for several types of functionals.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.467-474
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• 2022

In this article, we consider the integral operator 𝓒^b,c, which is defined as follows: $${\mathcal{C}}^{b,c}(f)(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}}dw,$$ where * denotes the Hadamard/ convolution product of power series, F(a, b; c; z) is the classical hypergeometric function with b, c > 0, b + 1 > c and f(0) = 0. We investigate the boundedness of the 𝓒^b,c operators on Bloch spaces.