scholarly journals On q-Hermite-Hadamard Inequalities for Differentiable Convex Functions

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 632 ◽  
Author(s):  
Seksan Jhanthanam ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Kamsing Nonlaopon
Keyword(s):  
Critical Point ◽  
Convex Functions ◽  
Hadamard Inequality ◽  
Left Hand ◽  
Point Type

In this paper, we establish some new results on the left-hand side of the q-Hermite–Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 2018, 30, 193-203), by considering the critical point-type inequalities.

POST QUANTUM-HERMITE-HADAMARD INEQUALITIES FOR DIFFERENTIABLE CONVEX FUNCTIONS WITH A CRITICAL POINT

2021 ◽  
Vol 21 (2) ◽  
pp. 337-346
Author(s):  
GHAZALA GULSHAN ◽  
RASHIDA HUSSAIN ◽  
ASGHAR ALI
Keyword(s):  
Convex Function ◽  
Critical Point ◽  
Convex Functions ◽  
Hadamard Inequality ◽  
Left Hand ◽  
Special Values ◽  
Special Cases

In this study, we obtained some new post quantum-Hermite-Hadamard inequalities for differentiable convex function with critical point by using generalized (p, q)- Hermite-Hadamard Inequality. The perseverance of this article is to establish different results on the left-hand side of (p,q)-Hermite-Hadamard inequality for differentiable convex function along with critical point. Special cases were obtained for different (p, q)-Hermite Hadamard inequalies with the critical point c for some special values of q.

scholarly journals Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 163 ◽  
Author(s):  
Shilpi Jain ◽  
Khaled Mehrez ◽  
Dumitru Baleanu ◽  
Praveen Agarwal
Keyword(s):  
Convex Functions ◽  
Harmonic Numbers ◽  
Positive Real ◽  
Hadamard Inequality ◽  
Left Hand ◽  
Polygamma Functions ◽  
Special Means ◽  
The Right ◽  
Logarithmically Convex Functions ◽  
New Inequalities

In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite–Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex. As an application, we derive certain inequalities involving the q-digamma and q-polygamma functions, respectively. As a consequence, new inequalities for the q-analogue of the harmonic numbers in terms of the q-polygamma functions are derived. Moreover, several inequalities for special means are also considered.

scholarly journals Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández
Keyword(s):  
Hypergeometric Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Quantum Calculation ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Quantum Integral

In this work, a study is conducted on the Hermite–Hadamard inequality using a class of generalized convex functions that involves a generalized and parametrized class of special functions within the framework of quantum calculation. Similar results can be obtained from the results found for functions such as the hypergeometric function and the classical Mittag–Leffler function. The method used to obtain the results is classic in the study of quantum integral inequalities.

scholarly journals Trapezium-Type Inequalities for an Extension of Riemann–Liouville Fractional Integrals Using Raina’s Special Function and Generalized Coordinate Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 117
Author(s):  
Miguel Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge Eliecer Hernández Hernández
Keyword(s):  
Convex Functions ◽  
Special Function ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Several Variables ◽  
Special Cases ◽  
Interesting Identity ◽  
Generalized Coordinate

In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite–Hadamard inequality for generalized coordinate ϕ-convex functions via an extension of the Riemann–Liouville fractional integral. Furthermore, an interesting identity for functions with two variables is obtained, and with the use of it, some new extensions of trapezium-type inequalities using Raina’s special function via generalized coordinate ϕ-convex functions are developed. Various special cases have been studied. At the end, a brief conclusion is given as well.

scholarly journals Hadamard Inequalities for Strongly α , m -Convex Functions via Caputo Fractional Derivatives

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Yanliang Dong ◽  
Muhammad Zeb ◽  
Ghulam Farid ◽  
Sidra Bibi
Keyword(s):  
Error Bounds ◽  
Convex Functions ◽  
Fractional Derivatives ◽  
Caputo Fractional Derivatives ◽  
Hadamard Inequality

In this paper, we present two versions of the Hadamard inequality for α , m convex functions via Caputo fractional derivatives. Several related results are analyzed for convex and m -convex functions along with their refinements and generalizations. The error bounds of the Hadamard inequalities are established by applying some known identities.

scholarly journals Generalized Hadamard Fractional Integral Inequalities for Strongly s , m -Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Chao Miao ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Yanhua Bian
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Hadamard Fractional Integral

This article deals with Hadamard inequalities for strongly s , m -convex functions using generalized Riemann–Liouville fractional integrals. Several generalized fractional versions of the Hadamard inequality are presented; we also provide refinements of many known results which have been published in recent years.

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