• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.57-66
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• 2009

In this paper, we characterize the boundedness and compactness of the extended $Ces{\grave{a}}ro$ operators from general function spaces F(p, q, s) to Bloch-type spaces ${\mathcal{B}}_{\mu}$ where $\mu$ is normal function on [0,1).

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1217-1227
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• 2018

In the paper, we study the growth and fixed point of solutions of high order linear differential equations with entire coefficients of [p, q]-order in the complex plane. We improve and extend some results due to T. B. Cao, J. F. Xu, Z. X. Chen, and J. Liu, J. Tu, L. Z. Shi.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.723-734
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• 2022

In this work, we introduce a new subclass of analytic functions of complex order involving the (p, q)-derivative operator defined in the open unit disc. For this class, several Fekete-Szegö type coefficient inequalities are derived. We obtain the results of Srivastava et al. [22] as consequences of the main theorem in this study.

• 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.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.71-84
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• 2007

J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.

• Korean Journal of Artificial Intelligence
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• v.5 no.1
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• pp.1-9
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• 2017

Recently, the Q-Learning algorithm, which is one kind of reinforcement learning, is mainly used to implement artificial intelligence system in combination with deep learning. Many research is going on to improve the performance of Q-Learning. Therefore, purpose of theory try to improve the performance of Q-Learning algorithm. This Theory apply Cross Entropy Error to the loss function of Q-Learning algorithm. Since the mean squared error used in Q-Learning is difficult to measure the exact error rate, the Cross Entropy Error, known to be highly accurate, is applied to the loss function. Experimental results show that the success rate of the Mean Squared Error used in the existing reinforcement learning was about 12% and the Cross Entropy Error used in the deep learning was about 36%. The success rate was shown.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.599-611
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• 2016

Let $k={\mathbb{F}}_q(t)$ be a rational function field over the finite field ${\mathbb{F}}_q$. In this paper we obtain formulas of average values of L-functions of some family of Artin-Schreier extensions over k.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1873-1882
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• 2017

We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of q-partite graphs of given order, size and number of connected components.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.601-612
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• 2016

In this paper we obtain average of class numbers of some family of Artin-Schreier extensions of rational function field ${\mathbb{F}}_q(t)$, where q is a power of 3.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.1-6
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• 2001

We discuss the value distribution of composite entire functions including those of infinite order and estimate the number of Q-points of such functions for an entire function Q or relatively slower growth.