Abstract
The main aim of this paper is to introduce a new class of harmonic convex functions with respect to non-negative function h, which is called generalized (h,r)-harmonic convex functions. We derive some new Fejer-Hermite-Hadamard type inequalities for generalized harmonic convex functions. Some special cases are also discussed. The ideas and techniques of this paper may stimulate further research.
Highlights
Convexity theory has become a rich source of inspiration in pure and applied sciences
The main aim of this paper is to introduce a new class of harmonic convex functions with respect to non-negative function h, which is called generalized (h, r)-harmonic convex functions
Gordji et al [3, 4] considered a new class of convex functions, which is called the generalized convex( φ-convex) functions
Summary
Convexity theory has become a rich source of inspiration in pure and applied sciences. We derive some new Fejer-Hermite-Hadamard type inequalities for generalized harmonic convex functions. Pearce et al [18] generalized the Hermite-Hadamard inequality to a r -convex positive functions.
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