Volume 7, Issue 3 (March 2020), Pages: 113-118

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 Original Research Paper

 Title: A weighted version of Hermite-Hadamard type inequalities for strongly GA-convex functions

 Author(s): Nidhi Sharma ¹, S. K. Mishra ¹, A. Hamdi ^2, *

 Affiliation(s):

 ¹Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India
 ²Department of Mathematics, Statistics and Physics College of Arts and Sciences, Qatar University, Doha, Qatar

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0003-1950-8907

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2020.03.012

 Abstract:

In this paper, we have established new weighted Hermite-Hadamard type inequalities for strongly GA-convex functions. Those findings are obtained by using geometric symmetry of continuous positive mappings and differentiable mappings whose derivative in absolute value are strongly GA-convex. Some previous results are special cases of the results obtained in this paper. 

 © 2020 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Convex function, Geometrically symmetric function, Strongly GA-convex function, Hermite Hadamard inequality, Holder inequality

 Article History: Received 11 October 2019, Received in revised form 6 January 2020, Accepted 7 January 2020

 Acknowledgment:

The authors would like to thank the anonymous reviewers for their helpful comments.

 Funding:

The research of the first author is supported by the UGC-BHU Research Fellowship, through sanction letter no: Ref No./Math/Res/Sept. 2017/117 and the second author is financially supported by the Department of Science and Technology, SERB, New Delhi, India, through grant no. MTR/2018/000121.

 Compliance with ethical standards

 Conflict of interest: The authors declare that they have no conflict of interest.

 Citation:

 Sharma N, Mishra SK, and Hamdi A (2020). A weighted version of Hermite-Hadamard type inequalities for strongly GA-convex functions. International Journal of Advanced and Applied Sciences, 7(3): 113-118

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 References (18) 

1. Dragomir SS and Pearce C (2003). Selected topics on Hermite-Hadamard inequalities and applications. Mathematics Preprint Archive, 2003(3): 463-817.   [Google Scholar]
2. Karamardian S (1969a). The nonlinear complementarity problem with applications, Part 1. Journal of Optimization Theory and Applications, 4(2): 87-98. https://doi.org/10.1007/BF00927414   [Google Scholar]
3. Karamardian S (1969b). The nonlinear complementarity problem with applications, Part 2. Journal of Optimization Theory and Applications, 4(3): 167-181. https://doi.org/10.1007/BF00930577   [Google Scholar]
4. Latif MA (2014). New Hermite–Hadamard type integral inequalities for GA-convex functions with applications. Analysis, 34(4): 379-389. https://doi.org/10.1515/anly-2012-1235   [Google Scholar]
5. Merentes N and Nikodem K (2010). Remarks on strongly convex functions. Aequationes Mathematicae, 80(1-2): 193-199. https://doi.org/10.1007/s00010-010-0043-0   [Google Scholar]
6. Niculescu C and Persson LE (2006). Convex functions and their applications. Springer, New York, USA. https://doi.org/10.1007/0-387-31077-0   [Google Scholar]
7. Niculescu CP (2000). Convexity according to the geometric mean. Mathematical Inequalities and Applications, 3(2): 155-167. https://doi.org/10.7153/mia-03-19   [Google Scholar]
8. Nikodem K and Páles Z (2011). Characterizations of inner product spaces by strongly convex functions. Banach Journal of Mathematical Analysis, 5(1): 83-87. https://doi.org/10.15352/bjma/1313362982   [Google Scholar]
9. Noor MA, Noor KI, and Awan MU (2014a). Geometrically relative convex functions. Applied Mathematics and Information Sciences, 8(2): 607-616. https://doi.org/10.12785/amis/080218   [Google Scholar]
10. Noor MA, Noor KI, and Awan MU (2014b). Some inequalities for geometricallyarithmetically h-convex functions. Creative Mathematics and Informatics, 23(1): 91-98.   [Google Scholar]
11. Noor MA, Noor KI, and Safdar F (2017). Generalized geometrically convex functions and inequalities. Journal of Inequalities and Applications, 2017: 202. https://doi.org/10.1186/s13660-017-1477-x   [Google Scholar] PMid:28932100 PMCid:PMC5575034
12. Obeidat S and Latif MA (2018). Weighted version of Hermite–Hadamard type inequalities for geometrically quasi-convex functions and their applications. Journal of Inequalities and Applications, 2018: 307. https://doi.org/10.1186/s13660-018-1904-7   [Google Scholar] PMid:30839800 PMCid:PMC6244744
13. Polyak BT (1966). Existence theorems and convergence of minimizing sequences in extremum problems with restrictions. Soviet Mathematics-Doklady, 7: 72-75.   [Google Scholar]
14. Qi F and Xi BY (2014). Some Hermite–Hadamard type inequalities for geometrically quasi-convex functions. Proceedings-Mathematical Sciences, 124(3): 333-342. https://doi.org/10.1007/s12044-014-0182-7   [Google Scholar]
15. Qi F, Wei ZL, and Yang Q (2005). Generalizations and refinements of Hermite-Hadamard's inequality. The Rocky Mountain Journal of Mathematics, 35(1): 235-251. https://doi.org/10.1216/rmjm/1181069779   [Google Scholar]
16. Shuang Y, Yin HP, and Qi F (2013). Hermite–Hadamard type integral inequalities for geometric-arithmetically s-convex functions. Analysis International Mathematical Journal of Analysis and Its Applications, 33(2): 197-208. https://doi.org/10.1524/anly.2013.1192   [Google Scholar]
17. Turhan S, Demirel AK, Maden S, and İşcan İ (2018). Hermite-Hadamard inequality for strongly GA-convex functions. Available online at: https://bit.ly/3bxhYnE
18. Zhang TY, Ji AP, and Qi F (2013). Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means. Le Matematiche, 68(1): 229-239.   [Google Scholar]