2018
DOI: 10.1186/s13660-018-1826-4
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Generalized Steffensen’s inequality by Lidstone interpolation and Montogomery’s identity

Abstract: By using a Lidstone interpolation, Green’s function and Montogomery’s identity, we prove a new generalization of Steffensen’s inequality. Some related inequalities providing generalizations of certain results given in (J. Math. Inequal. 9(2):481–487, 2015) have also been obtained. Moreover, from these inequalities, we formulate linear functionals and describe their properties.

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Cited by 4 publications
(3 citation statements)
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“…Now if we use the values of G δ (x,ũ) over the intervals [s, x] and [x, t], then the following result is valid (see [4] and [13]).…”
Section: Theorem 15 Let Q Imentioning
confidence: 95%
“…Now if we use the values of G δ (x,ũ) over the intervals [s, x] and [x, t], then the following result is valid (see [4] and [13]).…”
Section: Theorem 15 Let Q Imentioning
confidence: 95%
“…(A 2 ) For n ∈ N, n ≥ 3, let ψ : [0, d] → R be an n times differentiable function with ψ(0) = 0 and ψ (n-1) absolutely continuous on [0, d]. The first part of this section is the generalization of (5). For this, we start with the following theorem.…”
Section: Generalization Of Steffensen's Inequality By Generalized Monmentioning
confidence: 99%
“…To proceed further, we recall a nice generalization of Steffensen's inequality proved by Pečarić, see [11]. Following two lemmas will be useful in our construction as well, see [14,15].…”
Section: Introductionmentioning
confidence: 99%