Square mean asymptotically $$\varkappa$$-periodic solution for stochastic integro-differential equations via the degree of nondensifiability

Abstract In this paper, we explore square-mean asymptotically $$\varkappa$$ -periodic mild solutions from square mean $$\varkappa$$ -periodic limit for a stochastic integro-differential equations driven by Brownian motion, utilizing Grimmer’s resolvent and a version of Darbo’s fixed point theorem based on the degree of nondensifiability. Additionally, an example is given to illustrate our results.