scholarly journals Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
İmdat İşcan
Keyword(s):  
Convex Functions ◽  
Real Numbers ◽  
Absolute Value ◽  
Differentiable Functions ◽  
Special Means ◽  
Harmonically Convex Functions

A new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite-Hadamard and Simpson-like types for functions whose derivatives in absolute value at certain power are harmonically convex. Some applications to special means of real numbers are also given.

Hermite-Hadamard and simpson-like type inequalities for differentiable p-quasi-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5945-5953 ◽  
Author(s):  
İmdat İsçan ◽  
Sercan Turhan ◽  
Selahattin Maden
Keyword(s):  
Convex Functions ◽  
Real Numbers ◽  
Absolute Value ◽  
Special Means ◽  
Quasi Convexity

In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

scholarly journals Fractional Ostrowski type inequalities for differentiable harmonically convex functions

2021 ◽  
Vol 7 (3) ◽  
pp. 3939-3958
Author(s):  
Thanin Sitthiwirattham ◽  
◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Sotiris K. Ntouyas ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Special Means ◽  
Special Cases ◽  
Harmonically Convex Functions ◽  
New Inequalities

<abstract><p>In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and $ k $-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.</p></abstract>

scholarly journals Some integral inequalities for multiplicatively geometrically P-functions

2019 ◽  
Vol 9 (2) ◽  
pp. 216-222 ◽  
Author(s):  
Huriye Kadakal
Keyword(s):  
Integral Inequalities ◽  
Real Numbers ◽  
Absolute Value ◽  
General Identity ◽  
Differentiable Functions ◽  
Special Means

In this manuscript, by using a general identity for differentiable functions we can obtain new estimates on a generalization of Hadamard, Ostrowski and Simpson type inequalities for functions whose derivatives in absolute value at certain power are multiplicatively geometrically P-functions. Some applications to special means of real numbers are also given.

scholarly journals Some New Inequalities on Generalization of Hermite-Hadamard and Bullen Type Inequalities, Applications to Trapezoidal and Midpoint Formula

2021 ◽  
Vol 45 (4) ◽  
pp. 647-657
Author(s):  
İMDAT İŞCAN ◽  
◽  
TEKİN TOPLU ◽  
FATİH YETGİN ◽  
◽  
...  
Keyword(s):  
Error Estimates ◽  
Real Numbers ◽  
Absolute Value ◽  
General Identity ◽  
Differentiable Functions ◽  
Special Means ◽  
New Inequalities

In this paper, we give a new general identity for differentiable functions. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are convex. Some applications to special means of real numbers are also given. Finally, some error estimates for the trapezoidal and midpoint formula are addressed.

Hermite–Hadamard–Mercer-Type Inequalities for Harmonically Convex Mappings

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2556
Author(s):  
Xuexiao You ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Jiraporn Reunsumrit ◽  
Thanin Sitthiwirattham
Keyword(s):  
Convex Functions ◽  
Absolute Value ◽  
Convex Mappings ◽  
Special Means ◽  
Harmonically Convex Functions

In this paper, we prove Hermite–Hadamard–Mercer inequalities, which is a new version of the Hermite–Hadamard inequalities for harmonically convex functions. We also prove Hermite–Hadamard–Mercer-type inequalities for functions whose first derivatives in absolute value are harmonically convex. Finally, we discuss how special means can be used to address newly discovered inequalities.

scholarly journals On Ostrowski-Mercer inequalities for differentiable harmonically convex functions with applications

2021 ◽  
Author(s):  
Muhammad Aamir Ali ◽  
MUHAMMAD IMRAN ASJAD ◽  
Hüseyin BUDAK ◽  
Waqas FARIDI
Keyword(s):  
Convex Functions ◽  
Real Numbers ◽  
Special Means ◽  
Harmonically Convex Functions

In this work, we prove Ostrowski-Mercer inequalities for differentiable harmonically convex functions. It is also shown that the newly proved inequalities can be converted into some existing inequalities. Furthermore, it is provided that how the newly discovered inequalities can be applied to special means of real numbers.

scholarly journals Some New Post-Quantum Integral Inequalities Involving Twice (p,q)-Differentiable ψ-Preinvex Functions and Applications

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 283
Author(s):  
Miguel Vivas-Cortez ◽  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Artion Kashuri ◽  
Muhammad Aslam Noor
Keyword(s):  
Integral Identity ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Main Motivation ◽  
Absolute Value ◽  
Differentiable Functions ◽  
Quantum Integral ◽  
Special Means ◽  
Preinvex Functions

The main motivation of this article is derive a new post-quantum integral identity using twice (p,q)-differentiable functions. Using the identity as an auxiliary result, we will obtain some new variants of Hermite–Hadamard’s inequality essentially via the class of ψ-preinvex functions. To support our results, we offer some applications to a special means of positive real numbers and twice (p,q)-differentiable functions that are in absolute value bounded as well.

scholarly journals New Riemann–Liouville fractional Hermite–Hadamard type inequalities for harmonically convex functions

2019 ◽  
Vol 9 (2) ◽  
pp. 431-441
Author(s):  
Zeynep Şanlı ◽  
Mehmet Kunt ◽  
Tuncay Köroğlu
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Differentiable Functions ◽  
Left And Right ◽  
Harmonically Convex Functions

Abstract In this paper, we proved two new Riemann–Liouville fractional Hermite–Hadamard type inequalities for harmonically convex functions using the left and right fractional integrals independently. Also, we have two new Riemann–Liouville fractional trapezoidal type identities for differentiable functions. Using these identities, we obtained some new trapezoidal type inequalities for harmonically convex functions. Our results generalize the results given by İşcan (Hacet J Math Stat 46(6):935–942, 2014).

scholarly journals Fejér type integral inequalities related with geometrically-arithmetically convex functions with applications

2019 ◽  
Vol 23 (1) ◽  
pp. 51-64
Author(s):  
S. S. Dragomir ◽  
M. A. Latif ◽  
E. Momoniat
Keyword(s):  
Differentiable Function ◽  
Integral Inequality ◽  
Convex Functions ◽  
Symmetric Function ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Left Part ◽  
Special Means ◽  
Type Integral

A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fejér type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the Hölder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.

scholarly journals Some Fejér type integral inequalities for geometrically-arithmetically-convex functions with applications

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2193-2206 ◽  
Author(s):  
Muhammad Latif ◽  
Sever Dragomir ◽  
Ebrahim Momoniat
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Symmetric Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Type Integral

In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving geometrically symmetric functions is established, and by using the obtained identity, the H?lder integral inequality and the notion of geometrically-arithmetically convexity, some new Fej?r type integral inequalities are presented. Applications of our results to special means of positive real numbers are given as well.

Sign in / Sign up

Export Citation Format

Share Document