scholarly journals Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus

2021 ◽  
Vol 7 (3) ◽  
pp. 4266-4292
Author(s):  
Jorge E. Macías-Díaz ◽  
◽  
Muhammad Bilal Khan ◽  
Muhammad Aslam Noor ◽  
Abd Allah A. Mousa ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
The Other ◽  
Integral Inequalities ◽  
Generalized Convex Functions ◽  
Type Integral ◽  
The Subject ◽  
Harmonically Convex Functions ◽  
Interval Valued

<abstract> <p>The importance of convex and non-convex functions in the study of optimization is widely established. The concept of convexity also plays a key part in the subject of inequalities due to the behavior of its definition. The principles of convexity and symmetry are inextricably linked. Because of the considerable association that has emerged between the two in recent years, we may apply what we learn from one to the other. In this study, first, Hermite-Hadamard type inequalities for LR-$ p $-convex interval-valued functions (LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>) are constructed in this study. Second, for the product of p-convex various Hermite-Hadamard (<italic>HH</italic>) type integral inequalities are established. Similarly, we also obtain Hermite-Hadamard-Fejér (<italic>HH</italic>-Fejér) type integral inequality for LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>. Finally, for LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>, various discrete Schur's and Jensen's type inequalities are presented. Moreover, the results presented in this study are verified by useful nontrivial examples. Some of the results reported here for be LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic> are generalizations of prior results for convex and harmonically convex functions, as well as $ p $-convex functions.</p> </abstract>

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.

scholarly journals Novel Refinements via n –Polynomial Harmonically s –Type Convex Functions and Application in Special Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Saad Ihsan Butt ◽  
Saima Rashid ◽  
Muhammad Tariq ◽  
Miao-Kun Wang
Keyword(s):  
Convex Function ◽  
Hypergeometric Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Algebraic Properties ◽  
Type Integral ◽  
Harmonically Convex Functions ◽  
Formula Type

In this work, we introduce the idea of n –polynomial harmonically s –type convex function. We elaborate the new introduced idea by examples and some interesting algebraic properties. As a result, new Hermite–Hadamard, some refinements of Hermite–Hadamard and Ostrowski type integral inequalities are established, which are the generalized variants of the previously known results for harmonically convex functions. Finally, we illustrate the applicability of this new investigation in special functions (hypergeometric function and special mean of real numbers).

scholarly journals Generalizations of Hermite–Hadamard Type Integral Inequalities for Convex Functions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 136
Author(s):  
Ying Wu ◽  
Hong-Ping Yin ◽  
Bai-Ni Guo
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Type Integral ◽  
Integral Identities

In the paper, with the help of two known integral identities and by virtue of the classical Hölder integral inequality, the authors establish several new integral inequalities of the Hermite–Hadamard type for convex functions. These newly established inequalities generalize some known results.

scholarly journals Weighted Midpoint Hermite-Hadamard-Fejér Type Inequalities in Fractional Calculus for Harmonically Convex Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 252
Author(s):  
Humaira Kalsoom ◽  
Miguel Vivas-Cortez ◽  
Muhammad Amer Latif ◽  
Hijaz Ahmad
Keyword(s):  
Fractional Calculus ◽  
Convex Functions ◽  
Integral Identity ◽  
Fractional Integral ◽  
Symmetric Functions ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Type Integral ◽  
Harmonically Convex Functions

In this paper, we establish a new version of Hermite-Hadamard-Fejér type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Hadamard-Fejér type integral inequalities for harmonically convex functions by involving a positive weighted symmetric functions have been obtained. As shown, all of the resulting inequalities generalize several well-known inequalities, including classical and Riemann–Liouville fractional integral inequalities.

scholarly journals Hermite–Hadamard and Fractional Integral Inequalities for Interval-Valued Generalized p -Convex Function

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Zhengbo Li ◽  
Kamran ◽  
Muhammad Sajid Zahoor ◽  
Huma Akhtar
Keyword(s):  
Convex Function ◽  
Interval Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Interval Valued

In the present paper, the new interval-valued generalized p convex functions are introduced. By using the notion of interval-valued generalized p convex functions and some auxiliary results of interval analysis, new Hermite–Hadamard and Fejér type inequalities are proved. The established results are more generalized than existing results in the literature. Moreover, fractional integral inequality for this generalization is also established.

scholarly journals A note on Hadamard type integral inequalities involving several log-convex functions

2005 ◽  
Vol 36 (1) ◽  
pp. 43-47 ◽  
Author(s):  
B. G. Pachpatte
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Type Integral

In this note, two new inegral inequalities of Hadamard type involving several differentiable log-convex functions are given. Two refinements of Hadamard's integral inequality for log-convex functions recently established by Dragomir are shown to be recaptured as special instances.

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

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