scholarly journals A Note on Hermite–Hadamard–Fejer Type Inequalities for Functions Whose n-th Derivatives Are m-Convex or (α,m)-Convex Functions

Axioms ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 16
Author(s):  
Sanja Kovač
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Remainder Term ◽  
Quadrature Formulas ◽  
Differentiable Functions ◽  
Special Case

In this paper, we develop some Hermite–Hadamard–Fejér type inequalities for n-times differentiable functions whose absolute values of n-th derivatives are (α,m)-convex function. The results obtained in this paper are extensions and generalizations of the existing ones. As a special case, the generalization of the remainder term of the midpoint and trapezoidal quadrature formulas are obtained.

scholarly journals General Raina fractional integral inequalities on coordinates of convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Badreddine Meftah
Keyword(s):  
Mathematical Model ◽  
Fractional Calculus ◽  
Convex Function ◽  
Mathematical Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Differentiable Functions ◽  
Special Cases

AbstractIntegral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized Raina fractional integral inequalities using an $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates. Also, we obtain an integral identity for partial differentiable functions. As an effect of this result, two interesting integral inequalities for the $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates are given. Finally, we can say that our findings recapture some recent results as special cases.

scholarly journals New Quantum Estimates of Trapezium-Type Inequalities for Generalized ϕ-Convex Functions

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1047 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Rozana Liko ◽  
Artion Kashuri ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Trapezium Type ◽  
New Class ◽  
Differentiable Functions ◽  
Special Cases

In this paper, a quantum trapezium-type inequality using a new class of function, the so-called generalized ϕ -convex function, is presented. A new quantum trapezium-type inequality for the product of two generalized ϕ -convex functions is provided. The authors also prove an identity for twice q - differentiable functions using Raina’s function. Utilizing the identity established, certain quantum estimated inequalities for the above class are developed. Various special cases have been studied. A brief conclusion is also given.

scholarly journals Estimates of Mean-Type Fractional Inequalities For Differentiable Functions

2021 ◽  
Author(s):  
Muhammad Samraiz ◽  
Zahida Perveen ◽  
Sajid Iqbal ◽  
Saima Naheed ◽  
Thabet Abdeljawad
Keyword(s):  
Fractional Derivative ◽  
Convex Functions ◽  
Fractional Derivatives ◽  
Integral Inequalities ◽  
Hilfer Fractional Derivative ◽  
Caputo Fractional Derivatives ◽  
Differentiable Functions ◽  
Wide Range ◽  
Type Integral ◽  
Special Case

In this article, we established a wide range of fractional mean-type integral inequalities for notable Hilfer fractional derivative using twice differentiable convex and $s$-convex functions for $s\in(0,1]$ with related identities. Also the results for Caputo fractional derivatives are derived as a special case of our general results.

Some inequalities for exponentially convex functions on time scales

2021 ◽  
Vol 71 (4) ◽  
pp. 925-940
Author(s):  
Svetlin G. Georgiev ◽  
Vahid Darvish ◽  
Tahere A. Roushan
Keyword(s):  
Time Scales ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Double Inequality ◽  
Differentiable Functions ◽  
Classical Notion ◽  
Exponentially Convex Functions ◽  
Special Case ◽  
Class Of Functions

Abstract In this paper, we introduce the notion of exponentially convex functions on time scales and then we establish Hermite-Hadamard type inequalities for this class of functions. As special case, we derive this double inequality in the context of classical notion of exponentially convex functions and convex functions. Moreover, we prove some new integral inequalities for n-times continuously differentiable functions with exponentially convex first Δ-derivative.

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 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.

scholarly journals Simpson type inequalities and applications

2021 ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Michael Th. Rassias ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Identity ◽  
Higher Order ◽  
Auxiliary Result ◽  
First Order ◽  
New Class ◽  
Differentiable Functions

AbstractA new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of $$\sigma >0$$ σ > 0 . We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

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.

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