A generalization of Mercer’s result on convex functions

Niezgoda, Marek

doi:10.1016/j.na.2009.01.120

Cited by 57 publications

(40 citation statements)

References 7 publications

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“…One of them can be stated in Matkovic et al This study includes some new findings on Jensen's inequality of Mercer type for operators with applications [9]. Then, in 2009, Mercer's result was expanded to higher dimensions by Niezgoda's paper in [10]. Recently, notable contributions have been made on Jensen's Mercer type inequality.…”

Section: Theorem 11 If ϒ Is a Convex Function Onmentioning

confidence: 96%

Hermite–Jensen–Mercer type inequalities for conformable integrals and related results

et al. 2020

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Section: Theorem 11 If ϒ Is a Convex Function Onmentioning

confidence: 96%

Hermite–Jensen–Mercer type inequalities for conformable integrals and related results

et al. 2020

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“…The first and third members represent the Jensen-Mercer inequality obtained in [7], and its generalizations were reached in [6], [8], [3], [10], [5] and others. The proof of the inequality in formula (2.3) can be taken from the proof of Theorem 4.1.…”

Section: Convex Function and Its Double Discrete Inequalitiesmentioning

confidence: 99%

The Jensen-Mercer Inequality with Infinite Convex Combinations

Pavić¹

2019

Mathematical Sciences and Applications E-Notes

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“…There are many versions, variants, and generalizations of Propositions 1 and 2; see for example [4][5][6][7]. Here we state an integral version of Jensen's inequality from [1, pages 58-59] which will be needed in our main result.…”

Section: Proposition 2 Under the Assumptions Of Proposition 1 The Fmentioning

confidence: 99%

“…The following extension of inequality (2) was given by Niezgoda in [6] which is referred to as Niezgoda's inequality.…”

Section: Proposition 2 Under the Assumptions Of Proposition 1 The Fmentioning

confidence: 99%

Generalized Jensen-Mercer Inequality for Functions with Nondecreasing Increments

Khan

Saadi

2016

Abstract and Applied Analysis

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In the year 2003, McD Mercer established an interesting variation of Jensen’s inequality and later in 2009 Mercer’s result was generalized to higher dimensions by M. Niezgoda. Recently, Asif et al. has stated an integral version of Niezgoda’s result for convex functions. We further generalize Niezgoda’s integral result for functions with nondecreasing increments and give some refinements with applications. In the way, we generalize an important result, Jensen-Boas inequality, using functions with nondecreasing increments. These results would constitute a valuable addition to Jensen-type inequalities in the literature.

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A generalization of Mercer’s result on convex functions

Cited by 57 publications

References 7 publications

Hermite–Jensen–Mercer type inequalities for conformable integrals and related results

Hermite–Jensen–Mercer type inequalities for conformable integrals and related results

The Jensen-Mercer Inequality with Infinite Convex Combinations

Generalized Jensen-Mercer Inequality for Functions with Nondecreasing Increments

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