• Journal of applied mathematics & informatics
• /
• v.31 no.3_4
• /
• pp.577-594
• /
• 2013

In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.

• Journal of applied mathematics & informatics
• /
• v.30 no.5_6
• /
• pp.1051-1065
• /
• 2012

In this paper, the global stability and almost periodicity are investigated for generalized Hopfield neural networks with time-varying neutral delays. Some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results. Finally, an example is given to demonstrate the effectiveness of our results.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.199-207
• /
• 2009

This note is a verification on the relations between almost linear and nearly additive maps; and the continuity of almost multiplicative nearly additive maps. Also we consider the stability of nearly additive and almost linear maps.

• Journal of the Chungcheong Mathematical Society
• /
• v.15 no.1
• /
• pp.35-41
• /
• 2002

In this paper, we prove the stability of a Jensen's functional equation on a normed almost linear space.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.3
• /
• pp.561-568
• /
• 2011

We investigate the stability property and existence of almost periodic solutions of discrete Volterra equations with unbounded delay.

• Journal of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.445-459
• /
• 2006

In this paper cellular neural networks with continuously distributed delays are considered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using fixed point theorem, Lyapunov functional method and differential inequality technique. The results of this paper are new and they complement previously known results.

• Communications of the Korean Mathematical Society
• /
• v.19 no.2
• /
• pp.267-281
• /
• 2004

In this paper, we establish almost stability of Ishikawa iterative schemes with errors for the classes of Lipschitz $\phi$-strongly quasi-accretive operators and Lipschitz $\phi$-hemicontractive operators in arbitrary Banach spaces. The results of this paper extend a few well-known recent results.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.873-887
• /
• 2007

In this paper cellular neutral networks with time-varying delays and continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.1
• /
• pp.221-227
• /
• 2014

Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compared to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose.

• Journal of applied mathematics & informatics
• /
• v.10 no.1_2
• /
• pp.261-275
• /
• 2002

Let T be a local strongly accretive operator from a real uniformly smooth Banach space X into itself. It is proved that Ishikawa iterative schemes with errors converge strongly to a unique solution of the equations T$\_$x/ = f and x + T$\_$x/ = f, respectively, and are almost T$\_$b/-stable. The related results deal with the strong convergence and almost T$\_$b/-stability of Ishikawa iterative schemes with errors for local strongly pseudocontractive operators.