On some new Hardy‐type inequalities | Zendy

Benaissa Bouharket | Zendy; Sarikaya Mehmet Zeki | Zendy; Senouci Abdelkader | Zendy

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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,+ ∞ ).

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