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On some new Hardy‐type inequalities
Author(s) -
Benaissa Bouharket,
Sarikaya Mehmet Zeki,
Senouci Abdelkader
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6503
Subject(s) - mathematics , inequality , type (biology) , weight function , hardy space , function (biology) , pure mathematics , mathematical analysis , calculus (dental) , ecology , evolutionary biology , biology , medicine , dentistry
In this paper, we give some new types of the classical Hardy integral inequality by including a second parameter q and using weighted mean operatorsS 1 : = ( S 1 ) g wandS 2 : = ( S 2 ) g wdefined byS 1 ( x ) = 1 W ( x )∫ a x w ( t ) g ( f ( t ) ) d t ,S 2 ( x ) = ∫ a xw ( t ) W ( t ) g ( f ( t ) ) d t , with W ( x ) = ∫ 0 x w ( t ) d t , f o rx ∈ ( 0 , + ∞ ) , where w is a weight function and g is a real continuous function on (0,+ ∞ ).