• The Pure and Applied Mathematics
• /
• v.13 no.3 s.33
• /
• pp.227-236
• /
• 2006

The purpose of this paper is to establish a random fixed point theorem for nonconvex valued random multivalued operators, which generalize known results in the literature. We also derive a random coincidence fixed point theorem in the noncompart setting.

• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.425-434
• /
• 2007

We iteratively generate a sequence of measurable mappings and study necessary conditions for its convergence to a random fixed point of random nonexpansive operator. A random fixed point theorem for random nonexpansive operator, relaxing the convexity condition on the underlying space, is also proved. As an application, we obtained random fixed point theorems for Caristi type random operators.

• Journal of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.51-60
• /
• 2002

Some random fixed point theorems for nonexpansive and *-nonexpansive random operators defined on convex and star-shaped sets in a Frechet space are proved. Our work extends recent results of Beg and Shahzad and Tan and Yaun to noncontinuous multivalued random operators, sets analogue to an earlier result of Itoh and provides a random version of a deterministic fixed point theorem due to Singh and Chen.

• Kyungpook Mathematical Journal
• /
• v.56 no.2
• /
• pp.431-450
• /
• 2016

In this paper, the existence, uniqueness, stability via continuous dependence and Ulam stabilities of nonlinear integro-differential equations with random impulses are studied under sufficient condition. The results are obtained by using Leray-Schauder alternative fixed point theorem and Banach contraction principle.

• The Pure and Applied Mathematics
• /
• v.19 no.1
• /
• pp.59-71
• /
• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z)=0$$. by using a fixed point theorem in the sense of L. C$\breve{a}$dariu and V. Radu.

• Journal of Applied and Pure Mathematics
• /
• v.4 no.3_4
• /
• pp.107-122
• /
• 2022

This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsive neutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove the existence of mild solutions to this equation using the Banach fixed point theorem. Next, we demonstrate the stability via continuous dependence initial value. Our study extends the work of Wang, and Wu [16] where the time delay is addressed by the prescribed phase space 𝓑 (defined in Section 3). To illustrate the theory, we also provide an example of our methods. Using our results, one could investigate the controllability of random impulsive neutral stochastic differential equations with finite/infinite states. Moreover, one could extend this study to analyze the controllability of fractional-order of NRINSDEs with Poisson jumps as well.

• Communications of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.967-982
• /
• 2023

The goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.32 no.3
• /
• pp.280-289
• /
• 2008

This paper presents design of the quantitative feedback control system of the three axes hydraulic road simulator with respect to the dummy wheel for uncertain multiple input-output(MIMO) feedback systems. This simulator has the uncertain parameters such as fluid compressibility, fluid leakage, electrical servo components and nonlinear mechanical connections. This works have reproduced the random input signal to implement the real road vibration's data in the lab. The replaced $m^2$ MISO equivalent control systems satisfied the design specifications of the original $m^*m$ MIMO control system and developed the mathematical method using quantitative feedback theory based on schauder's fixed point theorem. This control system illustrates a tracking performance of the closed-loop controller with low order transfer function G(s) and pre-filter F(s) having the minimum bandwidth for parameters of uncertain plant. The efficacy of the designed controller is verified through the dynamic simulation with combined hydraulic model and Adams simulator model. The Matlab simulation results to connect with Adams simulator model show that the proposed control technique works well under uncertain hydraulic plant system. The designed control system has satisfied robust performance with stability bounds, tracking bounds and disturbance. The Hydraulic road simulator consists of the specimen, hydraulic pump, servo valve, hydraulic actuator and its control equipments