2020
DOI: 10.1155/2020/3945384
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Hermite-Hadamard- and Jensen-Type Inequalities for Interval h1,h2 Nonconvex Function

Abstract: In the present study, we will introduce the definition of interval h1,h2 nonconvex function. We will investigate some properties of interval h1,h2 nonconvex function. Moreover, we will develop Hermite-Hadamard- and Jensen-type inequalities for interval h1,h2 nonconvex function.

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Cited by 17 publications
(7 citation statements)
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“…e importance of convex functions and convex sets cannot be ignored, especially in nonlinear programing [1][2][3][4][5] and optimization theory [6], see, for instance, [7][8][9][10][11][12][13][14]. Generalization in the convexity is always appreciable.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…e importance of convex functions and convex sets cannot be ignored, especially in nonlinear programing [1][2][3][4][5] and optimization theory [6], see, for instance, [7][8][9][10][11][12][13][14]. Generalization in the convexity is always appreciable.…”
Section: Introductionmentioning
confidence: 99%
“…Also, many generalizations and extensions have been made in the theory of inequalities as well as in convexity. Several inequalities have been studied and established for the convexity of functions, and many generalizations, applications, and refinements take place, see [7,9,13,[15][16][17][18], for further study.…”
Section: Introductionmentioning
confidence: 99%
“…Later on, Costa et al [11] introduced generalized interval vector spaces and interval optimization. e convex functions in interval-valued calculus got attention of researchers due to its interesting geometric features and infimum properties [12][13][14][15]. is theory is also appealing for the applied engineers and programmes due to its applications in convex optimization [16][17][18].…”
Section: Introductionmentioning
confidence: 99%
“…In recent years, the researchers are working on fractional versions of mathematical inequalities by utilizing classical and new kinds fractional integral/derivative operators, see [8][9][10][11]. Also, several kinds of convex functions are applied to obtain these fractional versions, for example, see [1,[12][13][14][15][16][17] and references therein. The inequalities for fractional integrals and derivatives are very useful in the study of fractional differential equations.…”
Section: Introductionmentioning
confidence: 99%