The Riemann-Liouville Operator to Generate Some New Inequalities

where f, g are two differentiable functions and f ′, g′ ∈ L∞(a, b) and p is a positive and integrable function on [a, b]. Other interesting corollaries are also presented in [12]. Many researchers have given considerable attention to (1) and several inequalities related to this functional have appeared in the literature, to mention a few, see [1, 3, 8, 15, 16, 19, 20, 22] and the references cited therein. In the case of p is a constant function on [0,∞, [ we cite [9]; in this reference, there exist some new generalizations of [12]. In the case of the extended Chebyshev functional, using two positive integrable functions, we can cite [7, 10] in which we can find some interesting generalizations. The main aim of this paper is to establish some new inequalities for (1) by using the fractional integration theory. Some other ”no weighted” results are also presented. Our results, given in section 3, have some relationships with those obtained in [9, 12].