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1 Bulletin of the Polish Academy of Sciences. Mathematics

1 2002

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Integral inequalities associated with inequalities of Opial type

Florkiewicz B., Kuchta M.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 1

41-45

We derive some new integral inequalities of the form: [...], h [belongs to] H, where I = (alpha, beta), -[infinity is less than or equal alpha < beta is less than or equal infinity], p > 0, H is a wide class of absolutely continuous functions h defined on I and satisfying the limit conditions h(alpha) = 0 or h(beta) = 0, the functions r, s and u are any set of functions related by the appropriate weight functions. To get the desired inequality, at first we derive an integral inequality of Opial type using a uniform method of obtaining integral inequalities with weight functions involving the function and its derivative [2].