Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213120220301Extended Hermite-Hadamard $(H-H)$ and Fejer's inequalities based on $(h_1,h_2,s)$-convex functions28852895601510.22075/ijnaa.2022.6015ENSabir YasinDepartment of Mathematics and Statistics, School of Quantitative Sciences, Utara University, Malaysia, 06010 UUM Sintok, Kedah, MalaysiaMasnita MisiranDepartment of Mathematics and Statistics, School of Quantitative Sciences, Utara University, Malaysia, 06010 UUM Sintok, Kedah, MalaysiaCentre for Testing, Measurement and Appraisal, Utara University, Malaysia, 06010 UUM Sintok, Kedah, MalaysiaZurni OmarDepartment of Mathematics and Statistics, School of Quantitative Sciences, Utara University, Malaysia, 06010 UUM Sintok, Kedah, MalaysiaJournal Article20210912In 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