Hermite-Hadamard Inequalities for $\left(m,p\right) -$Earthquake Convex Functions
Abstract
In this paper, a new class of convex functions, referred to as $\left(m,p\right) -$earthquake convex functions, is introduced. For this class, several Hermite-Hadamard type inequalities are established, yielding explicit two-sided bounds in terms of endpoint values and special functions such as the Gamma and Beta functions. The obtained results provide refined integral estimates and unify a number of known inequalities associated with generalized convexity, thereby extending classical Hermite--Hadamard inequalities to a broader and more flexible framework.
Fields of Study & Subjects
Mathematical Inequalities and Applications
Analytic and geometric function theory
Optimization and Variational Analysis
Publication details
- Journal / source
- Communications in Advanced Mathematical Sciences
- Publisher
- Communications in Advanced Mathematical Sciences
- Volume
- 9
- Issue
- 1
- Pages
- 1–10
- Publication date
- 6 February 2026
- Language
- EN