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.

If f : [a,b] [right arrow] R is a

differentiable function with bounded derivative and [[alpha].

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.