The New Inequalities for tgs-Convex Functions
Download PDF
Authors: H. HUANG AND GUO-JIN XU
DOI: 10.46793/KgJMat2405.689H
Abstract:
In this paper, we establish some Hadamard-Hadamard type inequalities for tgs-convex functions. Our results are the generalizations of some known results. The new generalized estimate of the midpoints product of two tgs-convex functions is also considered.
Keywords:
Convexity, tgs-convexity, Hadamard-Hadamard-Fejér inequality.
References:
[1] L. Fejér, Über die Fourierreihen II, Anz Ungar. Akad. Wiss. 24 (1906), 369–360.
[2] S. Wu, On the weighted generalization of the Hermite-Hadamard inequality and its applications, Rocky Mountain J. Math. 39(5) (2009), 1741–1749. https://doi.org10.1216/RMJ-2009-39-5-1741
[3] F. X. Chen and X. F. Liu, Refinements on the Hermite-Hadamard inequalities for r-convex functions, J. Appl. Math. 2013 (2013), Article ID 978493, 5 pages. https://doi.org/10.1155/2013/978493
[4] Z. G. Xiao, Z. H. Zhang and Y. D. Wu, On weighted Hermite-Hadamard inequalities, Appl. Math. Comput. 218(3) (2011), 1147–1152. https://doi.org/10.1016/j.amc.2011.03.081
[5] M. Tunç, E. Göv and U. Şanal, On tgs-convex function and their inequalities, Facta Univ. Ser. Math. Inform. 30(5) (2015), 679–691.
[6] M. Tunç and U. Şanal, Some perturbed trapezoid inequalities for convex, s-convex and tgs-convex functions and applications, Tbilisi Math. J. 8(2) (2015), 87–102. https://doi.org/10.1515/tmj-2015-0013
[7] M. A. Noor, M. U. Awan, K. I. Noor and F. Safdar, Some new quantum inequalities via tgs-convex functions, TWMS J. Pure Appl. Math. 9(2) (2018), 135–146.
Login:
