Integro-quasidifferential equations (Q1874836)

The domain of the study of quasidifferential equations [cf. \textit{V. I. Zhegalov} and \textit{V. A. Sevast'yanov}, Differ. Uravn. 32, 1429--1430 (1996; Zbl 0896.35031)] includes differential equations, differential inclusions and equations with Hukuhara derivative and has produced results on integral funnel equations for differential inclusions. The author, in the present article, studies the existence and uniqueness theorem for integro-quasidifferential equations (or generalized quasidifferential equations) \[ d\left[ x(t+\Delta), q\left(\Delta,t,x(t), \int^t_{t_0} K\bigl( t,s,x(s)\bigr) ds \right)\right]= 0(\Lambda), \] \(d(\cdot,\cdot)\) being the distance in a complete metric space \(X\) for any continuous mapping \(f(t)\in Y\), \(Y\) is a metric space with metric \(\delta(\cdot,\cdot)\). Special cases of the uniqueness are also mentioned.