Abstract
The author introduces the concept of the P-GA-functions, gives Hermite-Hadamard's inequalities for P-GA-functions, and defines a new identity. By using this identity, the author obtains new estimates on generalization of Hadamard and Simpson type inequalities for P-GA-functions. Some applications to special means of real numbers are also given.
Highlights
Let real function f be defined on some nonempty interval I of real line R
Let f : I ⊆ (0, ∞) → R be a differentiable function on I∘, the interior of I; throughout this section we will take
Let f : I ⊆ (0, ∞) → R be a differentiable function on I∘ such that f ∈ L[a, b], where a, b ∈ I with a < b
Summary
Let real function f be defined on some nonempty interval I of real line R. The author introduces the concept of the P-GA-functions, gives Hermite-Hadamard’s inequalities for P-GA-functions, and defines a new identity. The author obtains new estimates on generalization of Hadamard and Simpson type inequalities for P-GA-functions. The function f is said to be convex on I if inequality f (tx + (1 − t) y) ≤ tf (x) + (1 − t) f (y) holds for all x, y ∈ I and t ∈ [0, 1].
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