scholarly journals Hermite–Hadamard-Type Inequalities for Product of Functions by Using Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Tariq Nawaz ◽  
M. Asif Memon ◽  
Kavikumar Jacob
Keyword(s):  
Convex Function ◽  
Finite Number ◽  
Convex Functions ◽  
The Many ◽  
The Given

One of the many techniques to obtain a new convex function from the given functions is to calculate the product of these functions by imposing certain conditions on the functions. In general, the product of two or finite number of convex function needs not to be convex and, therefore, leads us to the study of product of these functions. In this paper, we reframe the idea of product of functions in the setting of generalized convex function to establish Hermite–Hadamard-type inequalities for these functions. We have analyzed different cases of double and triple integrals to derive some new results. The presented results can be viewed as the refinement and improvement of previously known results.

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.

scholarly journals A note on generalized convex functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Syed Zaheer Ullah ◽  
Muhammad Adil Khan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Generalized Convex Functions

Abstract In the article, we provide an example for a η-convex function defined on rectangle is not convex, prove that every η-convex function defined on rectangle is coordinate η-convex and its converse is not true in general, define the coordinate $(\eta _{1}, \eta _{2})$(η1,η2)-convex function and establish its Hermite–Hadamard type inequality.

Continuity of h-convex functions

2019 ◽  
Vol 12 (04) ◽  
pp. 1950059
Author(s):  
M. Rostamian Delavar ◽  
S. S. Dragomir
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Continuity Condition

In this paper, a condition which implies the continuity of an [Formula: see text]-convex function is investigated. In fact, any [Formula: see text]-convex function bounded from above is continuous if the function [Formula: see text] satisfies a certain condition which is called pre-continuity condition.

Some Hermite-Hadamard type inequalities for convex functions via conformable fractional integrals and related inequalities

2017 ◽  
Vol 26 (2) ◽  
pp. 221-229
Author(s):  
ERHAN SET ◽  
MEHMET ZEKI SARIKAYA ◽  
ABDURRAHMAN GOZPINAR
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
The Given

In this present study, firstly we give some necessary definitions and some results related to Riemann-Liouville fractional and conformable fractional integrals. Secondly, using the given definitions , we established a new identity and Hermite-Hadamard type inequalities via conformable fractional integrals. Relevant connections of the results presented here with those earlier ones are also pointed out.

scholarly journals Conformable Fractional Integrals Versions of Hermite-Hadamard Inequalities and Their Generalizations

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Adil Khan ◽  
Yu-Ming Chu ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Gohar Ali
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Montgomery Identity

We prove new Hermite-Hadamard inequalities for conformable fractional integrals by using convex function, s-convex, and coordinate convex functions. We prove new Montgomery identity and by using this identity we obtain generalized Hermite-Hadamard type inequalities.

scholarly journals On Ostrowski-Mercer inequalities for differentiable convex function

2021 ◽  
Author(s):  
Muhammad Aamir Ali ◽  
Ifra Bashir Sial ◽  
Hüseyin BUDAK
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Ostrowski Inequality ◽  
Special Means

In this note, for differentiable convex functions, we prove some new Ostrowski-Mercer inequalities. These inequalities generalize an Ostrowski inequality and related inequalities proved in [3,5]. Some applications to special means are also given.

scholarly journals On the Hermite-Hadamard inequalities for h-convex functions on balls and ellipsoids

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5871-5886
Author(s):  
Xiaoqian Wang ◽  
Jianmiao Ruan ◽  
Xinsheng Ma
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
High Dimensional

In this paper, we establish some Hermite-Hadamard type inequalities for h- convex function on high-dimensional balls and ellipsoids, which extend some known results. Some mappings connected with these inequalities and related results are also obtained.

scholarly journals Stopping the Mobile Robotic Vehicle at a Defined Distance from the Obstacle by Means of an Infrared Distance Sensor

Sensors ◽  
2021 ◽  
Vol 21 (17) ◽  
pp. 5959
Author(s):  
Frantisek Klimenda ◽  
Roman Cizek ◽  
Matej Pisarik ◽  
Jan Sterba
Keyword(s):  
Experimental Data ◽  
Industry 4.0 ◽  
Autonomous Control ◽  
Front Part ◽  
Distance Sensor ◽  
The Creation ◽  
Robotic Vehicle ◽  
The Many ◽  
The Given

The article deals with the creation of a program for stopping an autonomous robotic vehicle Robotino® 4. generation at a defined distance from an obstacle. One of the nine infrared distance sensors located on the frame of the robotic vehicle in the front part of the frame is used for this application task. The infrared distance sensor characteristic is created from the measured experimental data, which is then linearized in the given section. The main aim of the experiment is to find such an equation of a line that corresponds to the stopping of a robotic vehicle with a given accuracy from an obstacle. The determined equation of the line is applied to the resulting program for autonomous control of the robotic vehicle. This issue is one of the many tasks performed by AGV in the industry. The introduction of AGVs into the industry is one of the many possibilities within Industry 4.0.

GENERALIZED h-CONVEXITY ON FRACTAL SETS AND SOME GENERALIZED HADAMARD-TYPE INEQUALITIES

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050021 ◽  
Author(s):  
WENBING SUN
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Generalized Convex Functions ◽  
Text Type ◽  
Fractal Sets ◽  
Type Concept ◽  
Real Linear

In this paper, we introduce the [Formula: see text]-type concept of generalized [Formula: see text]-convex function on real linear fractal sets [Formula: see text], from which the known definitions of generalized convex functions and generalized [Formula: see text]-convex functions are derived, and from this, we obtain generalized Godunova–Levin functions and generalized [Formula: see text]-functions. Some properties of generalized [Formula: see text]-convex functions are discussed. Lastly, some generalized Hadamard-type inequalities of these classes functions are given.

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