TY  - JOUR
T1  - Generalized $(H,\phi )$-Convexity and New Hermite-Hadamard Type Inequalities
AU  - Sarikaya, Mehmet Zeki
PY  - 2025
DA  - November
Y2  - 2025
DO  - 10.36753/mathenot.1778929
JF  - Mathematical Sciences and Applications E-Notes
JO  - Math. Sci. Appl. E-Notes
PB  - Murat TOSUN
WT  - DergiPark
SN  - 2147-6268
SP  - 201
EP  - 208
VL  - 13
IS  - 4
LA  - en
AB  - In this paper, we introduce a novel class of convex functions, called $(H,\phi)$-convex functions, defined via a general parametric mean $\phi$ and a weighting function $H$. This new convexity notion encompasses several well-known classes such as standard convexity, $s$-convexity, $h$-convexity, and $m$-convexity as particular cases. We provide illustrative examples demonstrating that this class is genuinely more general. Furthermore, we derive a new Hermite-Hadamard type inequality tailored to the $(H, \phi)$ -convex framework. Our results extend and unify various existing inequalities in the literature.
KW  - Convex function
KW  - $h$-convex function
KW  - $m$-convex function
KW  - $s$
-convex function
KW  - Hermite-Hadamard inequality
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UR  - https://doi.org/10.36753/mathenot.1778929
L1  - https://dergipark.org.tr/en/download/article-file/5218055
ER  -