The aim of this study is to introduce the notion of two-dimensional approximately harmonic (p₁,h₁) (p1,h1) - (p₂,h₂) (p2,h2) -convex functions. We show that the new class covers many new and known extensions of harmonic convex functions. We formulate several new refinements of Hermite–Hadamard like inequalities involving two-dimensional approximately harmonic (p₁,h₁) (p1,h1) - (p₂,h₂) (p2,h2) -convex functions. We discuss in detail the special cases that can be deduced from the main results of the paper.
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Butt et al. (2020) studied this question.
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