n-exponential convexity of weighted Hermite-Hadamard's inequality

Butt, Saad Ihsan; Jakšić, Rozarija; Kvesić, Ljiljanka; Pečarić, Josip

doi:10.7153/jmi-08-21

Cited by 5 publications

(2 citation statements)

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“…Problems faced in constrained control and estimation are convex. Geometrically, "the convex function is a real-valued function if the line segment joining any two of its points lies on or above the graph of the function in Euclidean space" [1,2].…”

Section: Introductionmentioning

confidence: 99%

Schur, Hermite-Hadamard, and Fejér Type Inequalities for the Class of Higher-Order Generalized Convex Functions

Saleem

Bashir

et al. 2022

Journal of Function Spaces

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The study of convex functions is an interesting area of research due to its huge applications in pure and applied mathematics special in optimization theory. The aim of this paper is to introduce and study a more generalized class of convex functions. We established Schur (S), Hermite-Hadamard (HH), and Fejér (F) type inequalities for introduced class of convex functions. The results presented in this paper extend and generalize many existing results of the literature.

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Section: Introductionmentioning

confidence: 99%

Schur, Hermite-Hadamard, and Fejér Type Inequalities for the Class of Higher-Order Generalized Convex Functions

Saleem

Bashir

et al. 2022

Journal of Function Spaces

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“…In [4,7,9,10,[13][14][15]18], the construction of m-exponentially convex functions is made through the method prescribed in [11]. The reader may refer to [6,16,17,21] for the background of exponential convexity and mean value theorems.…”

Section: (ψ(H)) − ψ(A(h))mentioning

confidence: 99%

Jessen type functionals and exponential convexity

Naeem¹,

Anwar²

2017

J. Math. Computer Sci.

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$q$ -Hermite–Hadamard Inequalities for Generalized Exponentially $(s, m;)$
Wang
¹
,
Kalsoom
²
,
Budak
³

et al. 2021
Journal of Mathematics
3
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0
0
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In this article, we introduce a new extension of classical convexity which is called generalized exponentially s , m ; η -preinvex functions. Also, it is seen that the new definition of generalized exponentially s , m ; η -preinvex functions describes different new classes as special cases. To prove our main results, we derive a new q m κ 2 -integral identity for the twice q m κ 2 -differentiable function. By using this identity, we show essential new results for Hermite–Hadamard-type inequalities for the q m κ 2 -integral by utilizing differentiable exponentially s , m ; η -preinvex functions. The results presented in this article are unification and generalization of the comparable results in the literature.

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n-exponential convexity of weighted Hermite-Hadamard's inequality

Abstract: Abstract. In this paper we construct n -exponentially convex functions and exponentially convex functions using the functional defined as the difference of the weighted Hermite-Hadamard's inequality for monotone functions.Mathematics subject classification (2010): 26D15.

Cited by 5 publications

References 4 publications

Schur, Hermite-Hadamard, and Fejér Type Inequalities for the Class of Higher-Order Generalized Convex Functions

Schur, Hermite-Hadamard, and Fejér Type Inequalities for the Class of Higher-Order Generalized Convex Functions

Jessen type functionals and exponential convexity

$q$ -Hermite–Hadamard Inequalities for Generalized Exponentially $(s, m;)$
Wang
¹
,
Kalsoom
²
,
Budak
³

et al. 2021
Journal of Mathematics
3
0
0
0
View full text Add to dashboard Cite

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n-exponential convexity of weighted Hermite-Hadamard's inequality

Abstract: Abstract. In this paper we construct n -exponentially convex functions and exponentially convex functions using the functional defined as the difference of the weighted Hermite-Hadamard's inequality for monotone functions.Mathematics subject classification (2010): 26D15.

Cited by 5 publications

References 4 publications

Schur, Hermite-Hadamard, and Fejér Type Inequalities for the Class of Higher-Order Generalized Convex Functions

Schur, Hermite-Hadamard, and Fejér Type Inequalities for the Class of Higher-Order Generalized Convex Functions

Jessen type functionals and exponential convexity

q -Hermite–Hadamard Inequalities for Generalized Exponentially s , m ; Wang1, Kalsoom2, Budak3 et al. 2021Journal of Mathematics3000View full textAdd to dashboardCite

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About

$q$ -Hermite–Hadamard Inequalities for Generalized Exponentially $(s, m;)$
Wang
¹
,
Kalsoom
²
,
Budak
³

et al. 2021
Journal of Mathematics
3
0
0
0
View full text Add to dashboard Cite