Improvement and generalization of some results related to the class of harmonically convex functions and applications
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Authors
Imran Abbas Baloch
- Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
- Higher Education Department, Govt. College Gulberg, Punjab, Pakistan.
Aqeel Ahmad Mughal
- Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan.
Yu Ming Chu
- Department of Mathematics, Huzhou University, Huzhou, China.
Absar Ul Haq
- Department of Basic Sciences and Humanities, University of Engineering and Technology (Narowal Campus), Lahore 54000, Pakistan.
Manuel De La Sen
- Institute of Research and Development of Processors, University of the Basque Country, campus of Leioa (Bizkaia), 48940 Leioa, Spain.
Abstract
Discrete Jensen-type inequality for a harmonically convex function was established by Dragomir in [S. S. Dragomir, RGMIA Monographs, Victoria University, (2015)]. In [I. A. Baloch, A. H. Mughal, Y. M. Chu, M. De la Sen, Accepted in Aims Mathematics], Baloch et al. presented a variant of discrete Jensen-type inequality for harmonically convex functions. Moreover, they established a Jensen-type inequality for harmonically \(h\)-convex functions, and then they proved the variant of Jensen-type inequality for harmonically \(h\)-convex functions. Our results generalize and improve some earlier results in the literature (for example see [S. S. Dragomir, RGMIA Monographs, Victoria University, (2015)] and [I. A. Baloch, A. H. Mughal, Y. M. Chu, M. De la Sen, Accepted in Aims Mathematics]) for the said class. Additionally, using them gives us more interesting results.
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ISRP Style
Imran Abbas Baloch, Aqeel Ahmad Mughal, Yu Ming Chu, Absar Ul Haq, Manuel De La Sen, Improvement and generalization of some results related to the class of harmonically convex functions and applications, Journal of Mathematics and Computer Science, 22 (2021), no. 3, 282--294
AMA Style
Baloch Imran Abbas, Mughal Aqeel Ahmad, Chu Yu Ming, Haq Absar Ul, Sen Manuel De La, Improvement and generalization of some results related to the class of harmonically convex functions and applications. J Math Comput SCI-JM. (2021); 22(3):282--294
Chicago/Turabian Style
Baloch, Imran Abbas, Mughal, Aqeel Ahmad, Chu, Yu Ming, Haq, Absar Ul, Sen, Manuel De La. "Improvement and generalization of some results related to the class of harmonically convex functions and applications." Journal of Mathematics and Computer Science, 22, no. 3 (2021): 282--294
Keywords
- Harmonically convex functions
- harmonically h-convex functions
- Jensen-type inequality
- a variant of Jensen-type inequality
- harmonic series
- HM-GM-AM inequality
- a variant of HM-GM-AM
MSC
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