Inequalities of the Type Hermite–Hadamard–Jensen–Mercer for Strong Convexity

Absolute Value ◽

Strongly Convex ◽

Differentiable Functions

By using the Jensen–Mercer inequality for strongly convex functions, we present Hermite–Hadamard–Mercer inequality for strongly convex functions. Furthermore, we also present some new Hermite‐Hadamard‐Mercer-type inequalities for differentiable functions whose derivatives in absolute value are convex.

Integral Majorization Type Inequalities for the Functions in the Sense of Strong Convexity

Journal of Function Spaces ◽

10.1155/2019/9487823 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11 ◽

Cited By ~ 3

Author(s):

Syed Zaheer Ullah ◽

Muhammad Adil Khan ◽

Zareen Abdulhameed Khan ◽

Yu-Ming Chu

Keyword(s):

Convex Functions ◽

Strong Convexity ◽

In this article, we establish several integral majorization type and generalized Favard’s inequalities for the class of strongly convex functions. Our results generalize and improve the previous known results.

Midpoint Inequalities via Strong Convexity Using Positive Weighted Symmetry Kernels

Journal of Function Spaces ◽

10.1155/2021/9653481 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Hengxiao Qi ◽

Waqas Nazeer ◽

Sami Ullah Zakir ◽

Kamsing Nonlaopon

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Strong Convexity ◽

In the present research, we generalize the midpoint inequalities for strongly convex functions in weighted fractional integral settings. Our results generalize many existing results and can be considered as extension of existing results.

On strongly convex functions

Carpathian Journal of Mathematics ◽

10.37193/cjm.2016.01.09 ◽

2016 ◽

Vol 32 (1) ◽

pp. 87-95

Author(s):

JUDIT MAKÓ ◽

◽

ATTILA HÁZY

Keyword(s):

Convex Functions ◽

Error Term ◽

Error Function ◽

Strong Convexity ◽

Type Function ◽

The main results of this paper give a connection between strong Jensen convexity and strong convexity type inequalities. We are also looking for the optimal Takagi type function of strong convexity. Finally a connection will be proved between the Jensen error term and an useful error function.

Generalization of Favard’s and Berwald’s Inequalities for Strongly Convex Functions

Communications in Mathematics and Applications ◽

10.26713/cma.v10i4.1210 ◽

2019 ◽

Vol 10 (4) ◽

Author(s):

Muhammad Adil Khan ◽

Syed Zaheer Ullah ◽

Yuming Chu

Keyword(s):

Convex Functions ◽

The second Hankel determinant for strongly convex and Ozaki close-to-convex functions

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/s10231-021-01089-3 ◽

2021 ◽

Author(s):

Young Jae Sim ◽

Adam Lecko ◽

Derek K. Thomas

Keyword(s):

Unit Disk ◽

Convex Functions ◽

Univalent Functions ◽

Inverse Function ◽

Invariance Property ◽

Hankel Determinant ◽

Sharp Bounds ◽

Strongly Convex ◽

Second Hankel Determinant

AbstractLet f be analytic in the unit disk $${\mathbb {D}}=\{z\in {\mathbb {C}}:|z|<1 \}$$ D = { z ∈ C : | z | < 1 } , and $${{\mathcal {S}}}$$ S be the subclass of normalized univalent functions given by $$f(z)=z+\sum _{n=2}^{\infty }a_n z^n$$ f ( z ) = z + ∑ n = 2 ∞ a n z n for $$z\in {\mathbb {D}}$$ z ∈ D . We give sharp bounds for the modulus of the second Hankel determinant $$ H_2(2)(f)=a_2a_4-a_3^2$$ H 2 ( 2 ) ( f ) = a 2 a 4 - a 3 2 for the subclass $$ {\mathcal F_{O}}(\lambda ,\beta )$$ F O ( λ , β ) of strongly Ozaki close-to-convex functions, where $$1/2\le \lambda \le 1$$ 1 / 2 ≤ λ ≤ 1 , and $$0<\beta \le 1$$ 0 < β ≤ 1 . Sharp bounds are also given for $$|H_2(2)(f^{-1})|$$ | H 2 ( 2 ) ( f - 1 ) | , where $$f^{-1}$$ f - 1 is the inverse function of f. The results settle an invariance property of $$|H_2(2)(f)|$$ | H 2 ( 2 ) ( f ) | and $$|H_2(2)(f^{-1})|$$ | H 2 ( 2 ) ( f - 1 ) | for strongly convex functions.