Some New Generalizations of Reverse Hilbert-Type Inequalities on Time Scales

被引：8

作者：

Rezk, Haytham M. ^{[1
]}

AlNemer, Ghada ^{[2
]}

Saied, Ahmed, I ^{[3
]}

Bazighifan, Omar ^{[4
]}

Zakarya, Mohammed ^{[5
,6
]}

机构：

[1] Al Azhar Univ, Fac Sci, Dept Math, Nasr City 11884, Egypt

[2] Princess Nourah Bint Abdulrahman Univ, Coll Sci, Dept Math Sci, POB 84428, Riyadh 11671, Saudi Arabia

[3] Benha Univ, Fac Sci, Dept Math, Banha 13518, Egypt

[4] Int Telemat Univ Uninettuno, Sect Math, Corso Vittorio Emanuele II 39, I-00186 Rome, Italy

[5] King Khalid Univ, Coll Sci, Dept Math, POB 9004, Abha 61413, Saudi Arabia

[6] Al Azhar Univ, Fac Sci, Dept Math, Assiut 71524, Egypt

来源：

SYMMETRY-BASEL | 2022年 / 14卷 / 04期

关键词：

reverse Hilbert-type inequalities; Specht's ratio; time scales; reverse Holder inequalities;

D O I：

10.3390/sym14040750

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This manuscript develops the study of reverse Hilbert-type inequalities by applying reverse Holder inequalities on T. We generalize the reverse inequality of Hilbert-type with power two by replacing the power with a new power beta, beta > 1. The main results are proved by using Specht's ratio, chain rule and Jensen's inequality. Our results (when T = N) are essentially new. Symmetrical properties play an essential role in determining the correct methods to solve inequalities.

引用

页数：24

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