Abstract
Abstract In this paper, authors establish a new identity for a differentiable function using generic integral operators. By applying it, some new integral inequalities of trapezium, Ostrowski and Simpson type are obtained. Moreover, several special cases have been studied in detail. Finally, many useful applications have been found.
Highlights
The paper is constructed in this way: In Section 2, we will find an interesting identity with parameter λ and using generic integral operators form auxiliary equality, some new integral inequalities of trapezium, Ostrowski and Simpson type will be obtain
Let Λ : P → R be a differentiable function on P◦ and λ ∈ R
Let Λ : P → R be a differentiable function on P◦ and λ ∈ [0, 1]
Summary
Λ((1 − ζ ) 1 + ζ 2) ≤ (1 − ζ )Λ( 1) + ζ Λ( 2), ∀ 1, 2 ∈ I, ζ ∈ [0, 1]. THEOREM 1.2. (Trapezium inequality) Suppose that Λ : I ⊆ R → R be a convex function, 1, 2 ∈ I with 1 < 2, . (Ostrowski inequality) Assume that Λ : I → R be a differentiable function on I◦, 1, 2 ∈ I◦ with 1 < 2. In our paper we will establish some new trapezium, Ostrowski and Simpson type inequalities pertaining generalized convex functions with respect to another function. For suitable choice of Fρσ,δ (·), we obtain definition 1.7. Sarikaya et al defined the following useful operators:. About their efficiency, see [18; 21; 45]. The paper is constructed in this way: In Section 2, we will find an interesting identity with parameter λ and using generic integral operators form auxiliary equality, some new integral inequalities of trapezium, Ostrowski and Simpson type will be obtain.
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