• Communications of the Korean Mathematical Society
• /
• 제10권2호
• /
• pp.461-469
• /
• 1995

Some bounds for anisotropic torsional rigidity with one plane of elastic symmetry perpendicular to the axis of the beam are derived by making use of the isoperimetric inequalities, complementary variational principles, and the maximum principle. Upper and lower bounds are obtained by applying the isoperimetric inequalities. While the upper bound investigated by the variational principles and maximum principle. The analysis is patterned after the work of Payne and Weinbeger [J. Math. Anal. Appl. 2(1961). pp. 210-216].

• Communications of the Korean Mathematical Society
• /
• 제32권4호
• /
• pp.875-883
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• 제28권3호
• /
• pp.635-642
• /
• 2013

There are many results on the extended operations of two fuzzy numbers based on the Zadeh's extension principle. For the calculation, we have to use existing operations between two ${\alpha}$-cuts. In this paper, we define parametric operations between two ${\alpha}$-cuts which are different from the existing operations. But we have the same results as the extended operations of Zadeh's principle.

• East Asian mathematical journal
• /
• 제27권5호
• /
• pp.585-595
• /
• 2011

In this paper, we introduce and study a new class of strongly nonlinear variational-like inequalities. Under suitable conditions, we prove the existence of solutions for the class of strongly nonlinear variational- like inequalities. By making use of the auxiliary principle technique, we suggest an iterative algorithm for the strongly nonlinear variational-like inequality and give the convergence criteria of the sequences generated by the iterative algorithm.

• Journal of the Korean Mathematical Society
• /
• 제38권2호
• /
• pp.283-296
• /
• 2001

The Heisenberg inequality associated with the uncertainty principle is extended to an infinite dimensional abstract Wiener space (H, B) with an abstract Wiener measure p$_1$. For $\phi$ $\in$ L$^2$(p$_1$) and T$\in$L(B, H), it is shown that (※Equations, See Full-text), where F(sub)$\phi$ is the Fourier-Wiener transform of $\phi$. The conditions when the equality holds also discussed.

• Communications of the Korean Mathematical Society
• /
• 제27권2호
• /
• pp.265-277
• /
• 2012

In this paper we establish two common fixed point theorems in fuzzy metric spaces. These theorems are generalisations of the Banach contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy metric spaces. Our result is also supported by examples.

• Journal of the Chungcheong Mathematical Society
• /
• 제24권2호
• /
• pp.253-266
• /
• 2011

We would like to generalize about trapezoidal fuzzy set and to calculate four operations based on the Zadeh's extension principle for two generalized trapezoidal fuzzy sets. And we roll up triangular fuzzy numbers and generalized triangular fuzzy sets into it. Since triangular fuzzy numbers and generalized triangular fuzzy sets are generalized trapezoidal fuzzy sets, we need no more the separate painstaking calculations of addition, subtraction, multiplication and division for two such kinds once the operations are done for generalized trapezoidal fuzzy sets.

• Journal of the Korean Mathematical Society
• /
• 제56권5호
• /
• pp.1419-1439
• /
• 2019

In this paper, we consider a class of noncooperative fourth-order elliptic systems involving nonlocal terms and critical growth in a bounded domain. With the help of Limit Index Theory due to Li [32] combined with the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity. Our results significantly complement and improve some recent results on the existence of solutions for fourth-order elliptic equations and Kirchhoff type problems with critical growth.

• Journal of the Korean Mathematical Society
• /
• 제56권4호
• /
• pp.935-946
• /
• 2019

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history. We consider Hawkes processes with uniform immigrants which is a special case of the Hawkes processes with renewal immigrants. We study the limit theorems for Hawkes processes with uniform immigrants. In particular, we obtain a law of large number, a central limit theorem, and a large deviation principle.

• Communications of the Korean Mathematical Society
• /
• 제37권2호
• /
• pp.521-535
• /
• 2022

In this paper, we introduce the k-Hankel-Wigner transform on R in some problems of time-frequency analysis. As a first point, we present some harmonic analysis results such as Plancherel's, Parseval's and an inversion formulas for this transform. Next, we prove a Heisenberg's uncertainty principle and a Calderón's reproducing formula for this transform. We conclude this paper by studying an extremal function for this transform.