• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권3호
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• pp.129-145
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• 2017

In this paper, we establish lower estimates for the modulus of the non-tangential derivative of the holomorphic functionf(z) at the boundary of the unit disc. Also, we shall give an estimate below |f''(b)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_0{\neq}0$.

• 대한수학회보
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• 제51권3호
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• pp.803-812
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• 2014

Let ${\mathcal{S}}^0_{\mathcal{H}}$ be the class of normalized univalent harmonic mappings in the unit disk. A subclass ${\mathcal{V}}^{\mathcal{H}}(k)$ of ${\mathcal{S}}^0_{\mathcal{H}}$, whose analytic part is function with bounded boundary rotation, is introduced. Some bounds for functionals, specially harmonic pre-Schwarzian derivative, described in ${\mathcal{V}}^{\mathcal{H}}(k)$ are given.

• 충청수학회지
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• 제28권4호
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• pp.583-590
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• 2015

This paper deals with linear impulsive fractional differential equations involving the Caputo derivative with non-integer order q. We provide exact solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions. Then we apply the exact solutions to improve impulsive integral inequalities with singularity.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.505-519
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• 2018

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

• East Asian mathematical journal
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• 제21권2호
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• pp.219-231
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• 2005

This paper investigates some results (Theorems 2.1-2.3, below) concerning certain classes of analytic and univalent functions, involving the familiar fractional derivative operators. We state interesting consequences arising from the main results by mentioning the cases connected with the starlikeness, convexity, close-to-convexity and quasi-convexity of geometric function theory. Relevant connections with known results are also emphasized briefly.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.193-209
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• 2021

In this research, we offer two new quantum integral equalities for recently defined qε2-integral and derivative, the derived equalities then used to prove quantum integral inequalities of Simpson's and Newton's type for preinvex functions. We also considered the special cases of established results and offer several new and existing results inside the literature of Simpson's and Newton's type inequalities.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.749-763
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• 2021

This research article deals with the Mittag-Leffler-Hyers-Ulam stability of linear and impulsive fractional order differential equation which involves the Caputo derivative. The application of the generalized fractional Fourier transform method and fixed point theorem, evaluates the existence, uniqueness and stability of solution that are acquired for the proposed non-linear problems on Lizorkin space. Finally, examples are introduced to validate the outcomes of main result.

• Journal of applied mathematics & informatics
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• 제41권1호
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• pp.167-179
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• 2023

In this paper, we investigate solutions of equations which are linear (p, q)-difference equation of higher order by using (p, q)-derivative and integral. We also derive the solution of equation in the case of second order.

• Korean Journal of Mathematics
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• 제31권1호
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• pp.25-33
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• 2023

This paper's objectives are to present the $\mathcal{H}$ class of analytical functions and explore the many characteristics of the functions that belong to this class. Some inequalities regarding the angular derivative have been discovered for the functions in this class. In addition, the symmetry points on the unit disc are used for the obtained inequalities.

• 대한수학회지
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• 제33권3호
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• pp.587-599
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• 1996

We assume throughout the paper that f(z) is a conformal function in the ipen unit disk $D = {z : $\mid$z$\mid$ < 1}$. In the rest of paper, conformal means analytic and locally univalent.