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The following theorem gives an Ostrowski type inequality for differentiable functions whose derivative in absolute value is preinvex.
Taking into account that ([theta] - [eta])/[psi] is an infinitely differentiable function with compact support and that F(([eta](1 - [phi]))/[psi]) [member of] [L.
Let f: I [right arrow] C be a differentiable function, and let [phi]: I [right arrow] [?
In the following, we let D be the space of infinitely differentiable functions [phi] with compact support and let D[a, b] be the space of infinitely differentiable functions with support contained in the interval [a, b].
For a complete study of subdifferentials of the functions obtained by algebraic operations with almost everywhere Frechet differentiable functions, we address the reader to the monograph [11], as well as to the research works [12], [13] and [14].
Let z be any differentiable function and define w by the Riccati substitution
Let f : [a, b] [right arrow] R be an n-time differentiable function, n [greater than or equal to] 1 and such that ||[f.
Thus we treat f ([xi], [eta], [zeta]) as a differentiable function of three variables, not two.
The differentiable function f on the [phi]-convex set K is said to be an [phi]-invex.
Choose a nowhere differentiable function b (for instance, a Weierstrass function ([9])) and [[alpha].
In 1981, Hanson [4] considered a differentiable function f: [R.