Abstract
Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as Jensen-type inequality for harmonic h -convex functions. In this paper, we aim to establish the functional form of inequalities presented by Baloch et al. and prove the superadditivity and monotonicity properties of these functionals. Furthermore, we derive the bound for these functionals under certain conditions. Furthermore, we define more generalized functionals involving monotonic nondecreasing concave function as well as evince superadditivity and monotonicity properties of these generalized functionals.
Highlights
Convexity is natural and simple notion which has found applications in business, industry, and medicine
Harmonic convex functions (HCFs) [1], harmonic (α, m)-convex functions [2], harmonic (s, m)-convex functions [3, 4], and harmonic (p, (s, m))-convex functions [5] are among these classes
Many researchers have been working on the class of harmonic convex functions (HCFs) due to its significance and have been trying to explore about it more and more
Summary
Convexity is natural and simple notion which has found applications in business, industry, and medicine. Recently different generalizations of the class of harmonic convex functions (HCFs) have been found, for example, see [10,11,12,13] and references therein. If we reverse the above inequality, the function f becomes harmonic concave.
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