Improved Jensen's type inequality for $(p,h)$-convex functions via Weak sub-majorization

Abstract

In this paper, we present several new inequalities for $(p,h)$-convex functions in a way that complements those known inequalities for $(p,h)$-convex functions due to M. A. Ighachane et al. (Filomat. \textbf{37}(16) (2023), 5259--5271). Further we mainly present some new inequalities for $(p,h)$-convex functions extending a key results of M. Sababheh. (Math. Inequal. Appl. \textbf{20}(2) (2017), 389--403).