On some new Hardy‐type inequalities. (12th May 2020)

• Record Type: Journal Article
• Authors: Benaissa, Bouharket; Sarikaya, Mehmet Zeki; Senouci, Abdelkader
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 15(2020)
• Page Start: 8488
• Page End: 8495
• Publication Date: 2020-05-12
• Subjects: Hardy‐type integral inequality -- Hölder's inequality -- weight function; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6503
• Languages: English
• ISSNs: 0170-4214

Abstract

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, + ∞ ).