• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1103-1114
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• 2023

The aim of the present paper is to obtain some mapping properties of subordinations by certain univalent functions in the open unit disk associated with a family of linear operators. Moreover, we also consider some applications for integral operators.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.303-315
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• 2014

In this work, we construct Kantorovich type generalization of a class of linear positive operators via Riemann type q-integral. We obtain estimations for the rate of convergence by means of modulus of continuity and the elements of Lipschitz class and also investigate weighted approximation properties.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.695-703
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• 2015

Several interesting and useful extensions of some familiar special functions such as Beta and Gauss hypergeometric functions and their properties have, recently, been investigated by many authors. Motivated mainly by those earlier works, we establish some fractional integral formulas involving the extended generalized Gauss hypergeometric function by using certain general pair of fractional integral operators involving Gauss hypergeometric function $_2F_1$, Some interesting special cases of our main results are also considered.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.387-395
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• 2015

We investigate conditions under which a holomorphic self-map of the unit disk induces a bounded composition operator and study some properties of the composition operator from the Bloch-type spaces into a generalization of the Bloch-type spaces.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.671-681
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• 2014

In this paper, we consider general Beta operators, which is a general sequence of integral type operators including Beta function. We study the King type Beta operators which preserves the third test function $x^2$. We obtain some approximation properties, which include rate of convergence and statistical convergence. Finally, we show how to reach best estimation by these operators.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.377-387
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• 2006

In this paper, we study the $L^p$ mapping properties of singular integral operators related to homogeneous mappings on product spaces with kernels which belong to $L(log^+\;L)^2$. Our results extend as well as improve some known results on singular integrals.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.41-50
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• 2021

This paper devoted to obtain some fractional integral properties of generalized Bessel function using pathway fractional integral operator. We also find the pathway transform of the generalized Bessel function in terms of Fox H-function.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.397-409
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• 2015

This paper considers a class of new convolution integral equations whose kernels involve special functions such as the generalized Mittag-Leffler function and the extended Kummer hypergeometric function. Some basic properties of interconnection with the familiar Riemann-Liouville operators are obtained which are used in fiding the solution of the main convolution integral equation. Several consequences are deduced from the main result by incorporating certain extended forms of hypergeometric functions in our present investigation.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.169-182
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• 2011

The main object of this paper is to introduce and investigate new subclasses of normalized analytic functions in the open unit disc $\mathbb{U}$, which generalize the familiar class of k-starlike functions. The various properties and characteristics for functions belonging to these classes derived here include (for example) coefficient inequalities, distortion theorems involving fractional calculus, extreme points, integral operators and integral means inequalities.

• Advances in Computational Design
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• v.9 no.1
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• pp.73-80
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• 2024

The aim of this paper is to remove the rigid body motion in the interior boundary value problem (BVP) of plane elasticity by solving the interior and exterior BVPs simultaneously. First, we formulate the interior and exterior BVPs simultaneously. The tractions applied on the contour in two problems are the same. After adding and subtracting the two boundary integral equations (BIEs), we will obtain a couple of BIEs. In the coupled BIEs, the properties of relevant integral operators are modified, and those integral operators are generally invertible. Finally, a unique solution for boundary displacement of interior region can be obtained.