In this paper, the exponential dichotomy, and Tikhonov and Banach fixed point theorems are used to study the existence and uniqueness of pseudo almost periodic solutions of a class of iterative functional differential equations of the form $$\begin{array}{} \displaystyle x'(t)=\sum_{n=1}^k\sum_{l=1}^\infty C_{l, n}(t)(x^{[n]}(t))^l+G(t), \end{array}$$ where x[n](t) denotes nth iterate of x(t).

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In this paper, we use Krasnoselskii's fixed point theorem to study the existence and uniqueness of periodic solutions of an iterative functional differential equation x′(t)=c1(t)x(t)+c2(t)x[2](t)+…+cn(t)x[n](t)+F(t). Copyright © 2016 John Wiley & Sons, Ltd.

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