Title: Some results in stochastic functional integro-differential equations with infinite delays

Authors: Arumugam Vinodkumar

Addresses: Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham University, Coimbatore 641 112, India

Abstract: In this paper, we study the results on averaging principle and stability of mild solutions for stochastic functional integro-differential equation with non-Lipschitz condition. We establish the result by the method of successive approximation and Bihari's inequality under the theory of resolvent operators. Finally, an example is provided for demonstration.

Keywords: averaging principle; Bihari's inequality; existence; resolvent operator; stability; successive approximation; uniqueness.

DOI: 10.1504/IJDSDE.2017.083726

International Journal of Dynamical Systems and Differential Equations, 2017 Vol.7 No.1, pp.36 - 50

Received: 01 Mar 2016
Accepted: 22 Aug 2016
Published online: 20 Apr 2017 *

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