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On approximately harmonic h-convex functions depending on a given function

Awan Muhammad Uzair (Mathematics Department, GC University, Faisalabad, Pakistan)
Noor Muhammad Aslam (Mathematics Department, COMSATS University Islamabad, Park Road, Islamabad, Pakistan)
Mihai Marcela V. (Department scientific-methodical sessions, Romanian Mathematical Society-branch Bucharest, Bucharest, Romania)
Noor Khalida Inayat (Mathematics Department, COMSATS University Islamabad, Park Road, Islamabad, Pakistan)
Akhtar Nousheen (Mathematics Department, GC University, Faisalabad, Pakistan)

A new class of harmonic convex function depending on given functions which is called as ”approximately harmonic h-convex functions” is introduced. With the discussion of special cases it is shown that this class unifies other classes of approximately harmonic h-convex function. Some associated integral inequalities with these new classes of harmonic convexity are also obtained. Several special cases of the main results are also discussed.

Keywords: convex, approximately, harmonic convex function, Hermite-Hadamard, inequalities