• Journal of the Chungcheong Mathematical Society
• /
• v.15 no.2
• /
• pp.73-84
• /
• 2003

In this paper, we investigate the new quadratic type functional equation f(2x + y) - f(x + 2y) = 3f(x) - 3f(y) and prove the stablility of this equation in the spirit of Hyers, Ulam, Rassias and G$\breve{a}$vruţa.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.523-535
• /
• 2012

In this paper, we investigate a fuzzy version of stability for the functional equation $$2f(x+y)+f(x-y)+f(y-x)-3f(x)-f(-x)-3f(y)-f(-y)=0$$ in the sense of M. Mirmostafaee and M. S. Moslehian.

• Korean Journal of Mathematics
• /
• v.23 no.3
• /
• pp.393-399
• /
• 2015

W. Park [J. Math. Anal. Appl. 376 (2011) 193-202] proved the Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. But there are serious problems in the control functions given in all theorems of the paper. In this paper, we correct the statements of these results and prove the corrected theorems. Moreover, we prove the superstability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces under the original given conditions.

• Kyungpook Mathematical Journal
• /
• v.55 no.4
• /
• pp.893-907
• /
• 2015

The Hyers-Ulam-Rassias stability of the k-th partial ternary quadratic derivations is investigated in non-Archimedean Banach ternary algebras and non-Archimedean $C^*$-ternary algebras by using the fixed point theorem.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2004.04a
• /
• pp.133-136
• /
• 2004

This paper proposes a stability condition in affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties and then, introduces the design method of a fuzzy-model-based controller which guarantees the stability. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of linear matrix inequalities (LMIs).

• Kyungpook Mathematical Journal
• /
• v.47 no.1
• /
• pp.91-103
• /
• 2007

In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ${\varphi}$ is defined by $f(x{\ast}y)+f(x{\ast}y^{-1})-2g(x)-2g(y)={\varphi}(x,y)$, $f(x{\ast}y)+g(x{\ast}y^{-1})-2h(x)-2k(y)={\varphi}(x,y)$, where (G, *) is a group, X is a real or complex Hausdorff topological vector space and f, g, h, k are functions from G into X.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.499-499
• /
• 2000

The robust stability problems for nominally linear system with nonlinear, structured perturbations arc considered with Lyapunov direct method. The Lyapunov direct method has been utilized to determine the bounds for nonlinear, time-dependent functions which can be tolerated by a stable nominal system. In most cases quadratic forms are used either as components of vector Lyapunov function or as a function itself. The resulting estimates are usually conservative. As it is known, often the conservatism of the bounds we propose to use a piecewise quadratic Lyapunov function. An example demonstrates application of the proposed method.

• The Pure and Applied Mathematics
• /
• v.12 no.2 s.28
• /
• pp.133-142
• /
• 2005

Generalizing the Cauchy-Rassias inequality in [Th. M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300.] we consider a stability problem of quadratic functional equation in the spaces of generalized functions such as the Schwartz tempered distributions and Sato hyperfunctions.

• Journal of the Chungcheong Mathematical Society
• /
• v.31 no.1
• /
• pp.89-101
• /
• 2018

In this paper, we consider the Hyers-Ulam stability on multi-valued dynamics. For a generalized n-dimensional quadratic set-valued functional equation, we prove the Hyers-Ulam stability for the functional equation in multi-valued dynamics.

• Communications of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.127-135
• /
• 2024

In this paper, we improve Corollary 1 of [4] and then present an example to show that the assertion in the mentioned corollary can not be valid in the singularity case.