A new version of Boole's formula type inequalities in multiplicative calculus with application to quadrature formula

被引:1
作者
Mateen, Abdul
Zhang, Zhiyue [1 ]
Toseef, Muhammad
Ali, Muhammad Aamir [1 ]
机构
[1] Hohai Univ, Sch Math, Nanjing 210098, Peoples R China
基金
中国国家自然科学基金;
关键词
Multiplicative calculus; Boole's formula; application to quadrature formula; multiplicatively convex function; HERMITE-HADAMARD TYPE; LOG-CONVEX FUNCTIONS; INTEGRAL-INEQUALITIES; DIFFERENTIABLE MAPPINGS; REAL NUMBERS;
D O I
10.36045/j.bbms.240612
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper presents a rigorous proof of novel multiplicative integral identity and utilize it to establish new Boole's type inequalities for multiplicatively convex functions. These newly established inequalities can be helpful in finding the bounds for Boole's formula within the framework of multiplicative calculus. Moreover, Boole's type inequalities provide best optimal approximations for polynomials of degree six. Finding an error term using the first derivative is an excellent achievement in inequality theory because the class of first-time differentiable functions is more extensive than that of bounded functions with six derivatives. Numerical examples and graphical analysis are conducted to validate the effectiveness of the newly derived findings. Furthermore, the derived results are applied to the quadrature formula and special means of real numbers, demonstrating their practical utility within the context of multiplicative calculus. This research highlights their potential impact on computational mathematics and related fields. The establishment of Boole's type inequalities for multiplicatively convex functions extends our understanding of inequalities in multiplicative calculus, opening avenues for future research and applications.
引用
收藏
页码:541 / 562
页数:22
相关论文
共 39 条
[1]  
Adnan Al-Alaoui M., 1996, SIGNUM Newsletter, V31, P25, DOI 10.1145/230922.230930
[2]   Study of Quantum Ostrowski-Type Inequalities for Differentiable Convex Functions [J].
Ali, M. A. ;
Feckan, M. ;
Mateen, A. .
UKRAINIAN MATHEMATICAL JOURNAL, 2023, 75 (01) :5-28
[3]  
Ali M.A., 2019, Asian Res. J. Math, V12, P1, DOI 10.9734/arjom/2019/v12i330084
[4]   On Simpson's and Newton's type inequalities in multiplicative fractional calculus [J].
Ali, Muhammad Aamir .
FILOMAT, 2023, 37 (30) :10133-10144
[5]  
Ali MA, 2019, J INEQUAL SPEC FUNCT, V10, P111
[6]  
Bai YM, 2016, J NONLINEAR SCI APPL, V9, P5900
[7]   Interpolating Jensen-type Operator Inequalities for Log-convex and Superquadratic Functions [J].
Bakherad, Mojtaba ;
Kian, Mohsen ;
Krnic, Mario ;
Ahmadi, Seyyed Alireza .
FILOMAT, 2018, 32 (13) :4523-4535
[8]   Multiplicative calculus and its applications [J].
Bashirov, Agamirza E. ;
Kurpinar, Emine Misirli ;
Ozyapici, Ali .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 337 (01) :36-48
[9]   ON HERMITE-HADAMARD TYPE INEQUALITIES FOR MULTIPLICATIVE FRACTIONAL INTEGRALS [J].
Budak, H. ;
Ozcelik, K. .
MISKOLC MATHEMATICAL NOTES, 2020, 21 (01) :91-99
[10]   FRACTIONAL HERMITE-HADAMARD-TYPE INEQUALITIES FOR INTERVAL-VALUED FUNCTIONS [J].
Budak, Huseyin ;
Tunc, Tuba ;
Sarikaya, Mehmet Zeki .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 148 (02) :705-718