Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 17 1 2026 01 01 Semi P-function and some new related inequalities 183 192 9489 10.22075/ijnaa.2023.30726.4474 EN Mahir Kadakal Bayburt University, Faculty of Applied Sciences, Department of Customs Management, Baberti Campus, 69000, Bayburt, TÜRKİYE İmdat İşcan Department of Mathematics, Sciences and Arts Faculty, Giresun University, 28100, Giresun, TÜRKİYE Huriye Kadakal Bayburt University, Faculty of Education, Department of Primary Education, Campus Baberti, 69000-Bayburt, Turkey Journal Article 2023 05 23 In this manuscript, we introduce and study the concept of semi P-functions and their some algebraic properties. Also, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power mean integral inequalities and show that the result obtained with Hölder-İşcan and improved power-mean inequalities give a better approach than the others. Some applications to special means of real numbers are also given. convex function semi P-function Hermite-Hadamard inequality Hölder-İşcan inequality improved power-mean inequality https://ijnaa.semnan.ac.ir/article_9489_b73799a20dcd51c47cf15c0bd440f4d3.pdf