scholarly journals On strongly convex functions

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 ◽  
Strongly Convex Functions ◽  
Strongly Convex

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.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Syed Zaheer Ullah ◽  
Muhammad Adil Khan ◽  
Zareen Abdulhameed Khan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Strong Convexity ◽  
Strongly Convex Functions ◽  
Strongly Convex

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.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Muhammad Adil Khan ◽  
Saeed Anwar ◽  
Sadia Khalid ◽  
Zaid Mohammed Mohammed Mahdi Sayed
Keyword(s):  
Convex Functions ◽  
Strong Convexity ◽  
Strongly Convex Functions ◽  
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.

scholarly journals Midpoint Inequalities via Strong Convexity Using Positive Weighted Symmetry Kernels

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 ◽  
Strongly Convex Functions ◽  
Strongly Convex

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.

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

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 Functions ◽  
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.

Bounds having Riemann type quantum integrals via strongly convex functions

2017 ◽  
Vol 54 (2) ◽  
pp. 221-240 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Gabriela Cristescu ◽  
Muhammad Uzair Awan
Keyword(s):  
Convex Functions ◽  
Strongly Convex Functions ◽  
Strongly Convex
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