On some new Hardy‐type inequalities. (12th May 2020) - Benaissa, Bouharket
Abstract : In this paper, we give some new types of the classical Hardy integral inequality by including a second parameter q and using weighted mean operators S 1 : = ( S 1 ) g w and S 2 : = ( S 2 ) g w defined by S 1 ( x ) = 1 W ( x ) ∫ a x w ( t ) g ( f ( t ) ) d t, S 2 ( x ) = ∫ a x w ( t ) W ( t ) g ( f ( t ) ) d t, with W ( x ) = ∫ 0 x w ( t ) d t, f o r x ∈ ( 0, + ∞ ), where w is a weight function and g is a real continuous function on (0, + ∞ ).