scholarly journals On Generalized Strongly p-Convex Functions of Higher Order

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Muhammad Shoaib Saleem ◽  
Yu-Ming Chu ◽  
Nazia Jahangir ◽  
Huma Akhtar ◽  
Chahn Yong Jung
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Higher Order ◽  
Definition Of

The aim of this paper is to introduce the definition of a generalized strongly p-convex function for higher order. We will develop some basic results related to generalized strongly p-convex function of higher order. Moreover, we will develop Hermite–Hadamard-, Fejér-, and Schur-type inequalities for this generalization.

scholarly journals Hermite-Hadamard Type Inequalities Associated with Coordinated((s,m),QC)-Convex Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Yu-Mei Bai ◽  
Shan-He Wu ◽  
Ying Wu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Type Integral ◽  
Definition Of

In this paper, we introduce the definition of coordinated((s,m),QC)-convex function and establish some Hermite-Hadamard type integral inequalities for coordinated((s,m),QC)-convex functions.

scholarly journals Operator (p, η)-Convexity and Some Classical Inequalities

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Chuanjun Zhang ◽  
Muhammad Shoaib Saleem ◽  
Waqas Nazeer ◽  
Naqash Shoukat ◽  
Yongsheng Rao
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Generalized Function ◽  
Basic Properties ◽  
Definition Of

In this paper, we will introduce the definition of operator p,η-convex functions, we will derive some basic properties for operator p,η-convex function, and also check the conditions under which operations’ function preserves the operator p,η-convexity. Furthermore, we develop famous Hermite–Hadamard, Jensen type, Schur type, and Fejér’s type inequalities for this generalized function.

Generalization of cyclic refinements of Jensen inequality by montgomery identity and Green’s function

2018 ◽  
Vol 11 (04) ◽  
pp. 1850060 ◽  
Author(s):  
Nasir Mehmood ◽  
Saad Ihsan Butt ◽  
Josip Pečarić
Keyword(s):  
Convex Function ◽  
Green’S Function ◽  
Green's Function ◽  
Convex Functions ◽  
Mean Value ◽  
Higher Order ◽  
Jensen Inequality ◽  
Linear Functionals ◽  
Montgomery Identity ◽  
Exponential Convexity

We consider discrete and continuous cyclic refinements of Jensen’s inequality and generalize them from convex function to higher order convex function by means of Lagrange Green’s function and Montgomery identity. We give application of our results by formulating the monotonicity of the linear functionals obtained from generalized identities utilizing the theory of inequalities for [Formula: see text]-convex functions at a point. We compute Grüss and Ostrowski type bounds for generalized identities associated with the obtained inequalities. Finally, we investigate the properties of linear functionals regarding exponential convexity log convexity and mean value theorems.

scholarly journals The Engulfing Property for Sections of Convex Functions on the Heisenberg Group and the Associated Quasi-distance

2021 ◽  
Author(s):  
A. Calogero ◽  
R. Pini
Keyword(s):  
Convex Function ◽  
Heisenberg Group ◽  
Convex Functions ◽  
Euclidean Case ◽  
Definition Of

AbstractIn this paper we investigate the property of engulfing for H-convex functions defined on the Heisenberg group $${\mathbb {H}^n}$$ H n . Starting from the horizontal sections introduced by Capogna and Maldonado (Proc Am Math Soc 134:3191–3199, 2006) , we consider a new notion of section, called $${\mathbb {H}^n}$$ H n -section, as well as a new condition of engulfing associated to the $${\mathbb {H}^n}$$ H n -sections, for an H-convex function defined in $$\mathbb {H}^n.$$ H n . These sections, that arise as suitable unions of horizontal sections, are dimensionally larger; as a matter of fact, the $${\mathbb {H}^n}$$ H n -sections, with their engulfing property, will lead to the definition of a quasi-distance in $${\mathbb {H}^n}$$ H n in a way similar to Aimar et al. in the Euclidean case (J Fourier Anal Appl 4:377–381, 1998). A key role is played by the property of round H-sections for an H-convex function, and by its connection with the engulfing properties.

scholarly journals m-Convex Functions of Higher Order

2020 ◽  
Vol 34 (2) ◽  
pp. 241-255
Author(s):  
Teodoro Lara ◽  
Nelson Merentes ◽  
Edgar Rosales
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Divided Difference ◽  
Higher Order

AbstractIn this research we introduce the concept of m-convex function of higher order by means of the so called m-divided difference; elementary properties of this type of functions are exhibited and some examples are provided.

scholarly journals New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating ℏ-Convex Functions in Hilbert Space

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 222 ◽  
Author(s):  
Saima Rashid ◽  
Humaira Kalsoom ◽  
Zakia Hammouch ◽  
Rehana Ashraf ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Convex Function ◽  
Convex Functions ◽  
Higher Order ◽  
Quasiconvex Functions ◽  
Auxiliary Result ◽  
Data Segmentation ◽  
Special Cases ◽  
Novel Variants ◽  
Convexity Theory

In Hilbert space, we develop a novel framework to study for two new classes of convex function depending on arbitrary non-negative function, which is called a predominating ℏ-convex function and predominating quasiconvex function, with respect to η , are presented. To ensure the symmetry of data segmentation and with the discussion of special cases, it is shown that these classes capture other classes of η -convex functions, η -quasiconvex functions, strongly ℏ-convex functions of higher-order and strongly quasiconvex functions of a higher order, etc. Meanwhile, an auxiliary result is proved in the sense of κ -fractional integral operator to generate novel variants related to the Hermite–Hadamard type for p t h -order differentiability. It is hoped that this research study will open new doors for in-depth investigation in convexity theory frameworks of a varying nature.

scholarly journals Inequalities for a Unified Integral Operator for Strongly α , m -Convex Function and Related Results in Fractional Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Chahn Yong Jung ◽  
Ghulam Farid ◽  
Kahkashan Mahreen ◽  
Soo Hak Shim
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Special Cases ◽  
Definition Of

In this paper, we study integral inequalities which will provide refinements of bounds of unified integral operators established for convex and α , m -convex functions. A new definition of function, namely, strongly α , m -convex function is applied in different forms and an extended Mittag-Leffler function is utilized to get the required results. Moreover, the obtained results in special cases give refinements of fractional integral inequalities published in this decade.

Some properties of convex functions

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 3015-3021
Author(s):  
Miloljub Albijanic
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Real Variable ◽  
First Derivative ◽  
Upper Limit ◽  
Definition Of

We treat two problems on convex functions of one real variable. The first one is concerned with properties of tangent lines to the graph of a convex function and essentially is related to the questions on the first derivative (if it exists). The second problem is related to Schwarz?s derivative, in fact its upper limit modification. It gives an interesting characterization of convex functions. Let us recall the definition of a convex functions.

Extreme-point solutions in Markov decision processes

1983 ◽  
Vol 20 (04) ◽  
pp. 835-842
Author(s):  
David Assaf
Keyword(s):  
Convex Function ◽  
Extreme Point ◽  
Markov Decision Processes ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Markov Decision ◽  
Full Solution

The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.

scholarly journals Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

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