Abstract
New Inequalities of Simpson’s type for differentiable functions via generalized convex function
Highlights
A well known definition in the mathematical literature is known as convex function: Definition 1
Let f be defined as in Theorem 19 and α = 1, m = 1, the inequality holds for convex functions: S
We have presented some new results related to Simpson’s type inequalities for powers in term of the first derivative using the (α, m)-convex functions
Summary
A well known definition in the mathematical literature is known as convex function: Definition 1. Many authors have been introduced new inequalities for convex functions but due to its large application and significance the well known Simpson’s inequality is stated as [1]: Let f : [a, b] → R be a four times continuously differentiable mapping on (a, b) and f (4) ∞ = sup f (4)(x) < ∞, x ∈(a,b) we have the following inequality:. Let f : [a, b] → R is a differentiable mapping whose derivative is continuous on (a, b) and f ∈ L1[a, b]. In [5], Kirmaci established the following Hermite–Hadamard type inequality for differentiable convex functions as: Theorem 4. The main aim of this paper is to establish new Simpson’s type inequalities for (α, m)- convexity for the class of functions whose derivatives in absolute value at certain powers are (α, m)−convex functions.
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