• 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.

• 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.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1111-1126
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• 2023

In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.359-376
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• 2020

The present research investigates the bounds of an integral operator for convex functions and a differentiable function f such that |f'| is convex. Further, these bounds of integral operators specifically produce estimations of various classical fractional and recently defined conformable integral operators. These results also contain bounds of Hadamard type for symmetric convex functions.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.309-318
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• 1996

The Gross Laplacian $\Delta_G$ was introduced by Groww for a function defined on an abstract Wiener space (H,B) [1,7]. Suppose $\varphi$ is a twice H-differentiable function defined on B such that $\varphi"(x)$ is a trace class operator of H for every x \in B.in B.

• Honam Mathematical Journal
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• v.29 no.1
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• pp.9-18
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• 2007

In this paper we establish the existence theorem of the operator-valued function space integral $K_{\lambda}(F)$ for $\lambda\in\mathbb{C}_{+,\lambda_0}^\sim$ where F is of the form (1.1). Our result is a generalization for Johnson and Skoug result in [8].

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.875-883
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• 2017

In this work, we establish Heisenberg-type uncertainty principle for the Bessel-Struve Fock space ${\mathbb{F}}_{\nu}$ associated to the Airy operator $L_{\nu}$. Next, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator $T:{\mathbb{F}}_{\nu}{\rightarrow}H$, where H be a Hilbert space. Furthermore, we come up with some results regarding the extremal functions, when T are difference operators.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.491-502
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• 2005

The main purpose of this paper is to extend the exponentially convex functions which are defined and exponentially convex on a cylinderical neighborhood in the Heisenberg group. They are expanded in terms of an integral transform associated to the sub-Laplacian operator. Extension of such functions on abelian Lie group are studied in [15].

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.13-22
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• 2019

This paper presents a symbolic method for solving a boundary value problem with inhomogeneous Stieltjes boundary conditions over integro-differential algebras. The proposed symbolic method includes computing the Green's operator as well as the Green's function of the given problem. Examples are presented to illustrate the proposed symbolic method.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.259-267
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• 2023

The paper presents the introduction of a novel linear derivative operator for meromorphic functions that are linked with q-calculus. Using the linear derivative operator, a new category of meromorphic functions is generated in the paper. We obtain sufficient conditions and show some properties of functions belonging to these subclasses. The partial sums of its sequence and the q-neighborhoods problem are solved.