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A function (fin BS^{p}(mathbb{R},X)) is called Stepanov-like weighted pseudo almost periodic if it can expressed as (f=h+varphi) where (h^{b}in AP mathbb{R},L^{p} 0, 1 X))) and (varphi^{b}in PAA_{0}(mathbb{R},L^{p}(0,1 X))).
A function (fin BS^{p}(mathbb{R},X)) is called Stepanov-like weighted pseudo almost automorphic if it can expressed as (f=h+varphi) where (h^{b}in AA(mathbb{R},L^{p}(0,1 X))) and (varphi^{b}in PAA_{0}(mathbb{R},L^{p}(0,1 X))).
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