Improved Jensen-type Inequalities for $(p,h)$-convex Functions with Applications
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Authors: M. A. IGHACHANE, L. SADEK AND M. SABABHEH
DOI: 10.46793/KgJMat2601.071I
Abstract:
The main goal of this article is to present multiple term refinements of the well-known Jensen’s inequality for h-convex functions for a non-negative super-multiplicative and super-additive function h. For example, we show that
h(1 − v)f(0) + h(v)f(1) ≥ f(v) + ∑
n=0N−1h(2r
n(v)) ∑
k=12n
Δf,h(0,1)(n,k)χ
 (v), |
for the h-convex function f and certain positive summands. The significance of the obtained results is the way they extend known results from the setting of convex functions to other classes of functions.
Keywords:
(p,h)-convex function, operator (p,h)-convex function, Jensen’s inequality.
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