• 호남수학학술지
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• 제39권2호
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• pp.307-315
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• 2017

In this paper, we aim to compare the differentials with the regularity of the hypercomplex valued functions in Clifford analysis. For three kinds of conjugation of the bicomplex numbers, we define the differentials of the bicomplex number functions by the naive approach. And we investigate some relations of the corresponding Cauchy-Riemann system and the conditions of the differentiable functions in the bicomplex number system.

• East Asian mathematical journal
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• 제27권1호
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• pp.51-65
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• 2011

In the paper, we study questions on classical solvability of nonlocal problems for a third-order linear hyperbolic equation in a rectangular domain. The Riemann method is applied to the Goursat problem and solution is obtained in the integral form. Investigated problems are reduced to the uniquely solvable Volterra-type equation of second kind. Influence effects of coefficients at lowest derivatives on correctness of studied problems are detected.

• 대한수학회보
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• 제58권3호
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• pp.537-557
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• 2021

In this paper, we investigate the curvature behavior of complete noncompact gradient expanding Ricci solitons with nonnegative Ricci curvature. For such a soliton in dimension four, it is shown that the Riemann curvature tensor and its covariant derivatives are bounded. Moreover, the Ricci curvature is controlled by the scalar curvature. In higher dimensions, we prove that the Riemann curvature tensor grows at most polynomially in the distance function.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.47-56
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• 2024

It is well known that inequalities enable us to analyze and solve complex problems with precision and efficiency. The inequalities provide powerful tools for establishing bounds, optimizing solutions, and deepening our understanding of mathematical concepts, paving the way for advancements in areas such as optimization, analysis, and probability theory. In this paper, we present some properties for Hadamard-Simpsons type inequalities in the classic integral and Riemann-Liouville fractional integral. We use the convexity of the given function and its first derivative.

• 호남수학학술지
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• 제30권4호
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• pp.671-676
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• 2008

We give the relation between the Riemann-Stieltjes integrals with respect to the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) distribution $H_{a,p}$ satisfying the equation a = $(1-a)^m$ and those with respect to the dual RNT distribution $H_{1-a,1-p}$, which leads to a generalization of recent results for a = $\frac{1}{2}$.

• 호남수학학술지
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• 제30권2호
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• pp.227-231
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• 2008

We give some relation between the Riemann-Stieltjes integrals with respect to the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) distribution $H_{a,p}$ satisfying the equation 1 - a = $a^m$ over different intervals, which generalizes recent results([6]) for a = ${\frac{1}{2}}$.

• East Asian mathematical journal
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• 제12권2호
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• pp.203-211
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• 1996

• 대한수학회보
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• 제53권2호
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• pp.507-518
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• 2016

In this paper, using forms of conjugations, we give some algebraic properties of bicomplex numbers. We research differential operators, elementary functions and the analogous Cauchy-Riemann system in bicomplex number systems. Also, we investigate the definition and properties of regular functions with values in bicomplex settings in Clifford analysis.

• East Asian mathematical journal
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• 제16권2호
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• pp.233-237
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• 2000

Since the time of Euler, there have been many proofs giving the value of $\zeta(2n)$. We also give an evaluation of $\zeta(2n)$ by analyzing the generating function of Bernoulli numbers.

• 충청수학회지
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• 제24권2호
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• pp.247-252
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• 2011

We study some properties of the Riemann-Stieltjes integrals with respect to the Riesz-$N\acute{a}gy$-$Tak\acute{a}cs$ distribution $H_{a,p}$ and its inverse $H_{p,a}$ on the unit interval satisfying the equation 1 - a = $a^2$ and p = 1 - a. Using the properties of the dual distributions $H_{a,p}$ and $H_{p,a}$, we compare the Riemann-Stieltjes integrals of $H_{a,p}$ over some essential intervals with that of its inverse $H_{p,a}$ over the related intervals.