positive real function

positive real function

[′päz·əd·iv ′rēl ′fəŋk·shən]
(mathematics)
An analytic function whose value is real when the independent variable is real, and whose real part is positive or zero when the real part of the independent variable is positive or zero.
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Here g is a positive real function of [C.sup.[infinity]]-class.
iii) F : I x [R.sup.n] [right arrow] KC([R.sup.n]) is an upper semicontinuous multifunction such that |F(t,x)| [less than or equal to] [alpha](t) + [beta](t)|x|, for every x [member of] C, for every t [member of] I and where t [right arrow] [alpha](t) and t [right arrow] [beta](t) are continuous positive real functions defined on I; (here |F(t,x)| = D(F(t,x),0));
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