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Abstract: In this paper, we study the mean square asymptotic stability of a class of generalized nonlinear stochastic Volterra–Levin equations by using fixed point theory. Several sufficient conditions are established for ensuring that the equation is mean square asymptotically stable as well as exponentially stable. The main results are new which generalize and improve some well-known results in Burton (2006) [4] and Luo (2010) [18]. Finally, two examples are given to illustrate our results. [Copyright &y& Elsevier]

Abstract: In this paper, a generalized Volterra–Levin equation is considered. 3/2-stability conditions are established for ensuring that the zero solution of the equation is uniformly stable, asymptotically stable and globally asymptotically stable. Further results are obtained under nonnegativity assumption. The main results are new and different from the known results. [Copyright &y& Elsevier]