Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 13 1 2022 03 01 Extended Hermite-Hadamard $(H-H)$ and Fejer's inequalities based on $(h_1,h_2,s)$-convex functions 2885 2895 6015 10.22075/ijnaa.2022.6015 EN Sabir Yasin Department of Mathematics and Statistics, School of Quantitative Sciences, Utara University, Malaysia, 06010 UUM Sintok, Kedah, Malaysia Masnita Misiran Department of Mathematics and Statistics, School of Quantitative Sciences, Utara University, Malaysia, 06010 UUM Sintok, Kedah, Malaysia Centre for Testing, Measurement and Appraisal, Utara University, Malaysia, 06010 UUM Sintok, Kedah, Malaysia Zurni Omar Department of Mathematics and Statistics, School of Quantitative Sciences, Utara University, Malaysia, 06010 UUM Sintok, Kedah, Malaysia Journal Article 2021 09 12 In this paper, $(h_1,h_2)$-convex and $s$-convex functions are merged to form $(h_1,h_2,s)$-convex function. Inequalities of the Hermite-Hadamard (H-H) and Fejer's types will then be extended by using the $(h_1,h_2,s)$-convex function and its derivatives. Some special cases for these extended H-H and Fejer's inequalities are also explored in order to get the previously specified results. The relationship between newly constructed Hermite-Hadamard $(H-H)$ and Fejer's types of inequalities with the average (mean) values are also discussed. https://ijnaa.semnan.ac.ir/article_6015_f31de2ea969c8c698a5215bea39db2ce.pdf