Integral Inequalities of the Hermite–Hadamard Type for K-Bounded Norm-Convex Mappings

2017 ◽  
Vol 68 (10) ◽  
pp. 1530-1551 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Integral Inequalities ◽  
Convex Mappings ◽  
Bounded Norm

scholarly journals New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1753
Author(s):  
Saima Rashid ◽  
Aasma Khalid ◽  
Omar Bazighifan ◽  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Convex Mappings ◽  
Special Cases ◽  
Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

scholarly journals New (p, q)-estimates for different types of integral inequalities via (α, m)-convex mappings

2020 ◽  
Vol 18 (1) ◽  
pp. 1830-1854
Author(s):  
Humaira Kalsoom ◽  
Muhammad Amer Latif ◽  
Saima Rashid ◽  
Dumitru Baleanu ◽  
Yu-Ming Chu
Keyword(s):  
Integral Identity ◽  
Integral Inequalities ◽  
First Order ◽  
Convex Mappings ◽  
Differentiable Functions ◽  
Different Types ◽  
Error Estimations ◽  
Quantum Error

Abstract In the article, we present a new ( p , q ) (p,q) -integral identity for the first-order ( p , q ) (p,q) -differentiable functions and establish several new ( p , q ) (p,q) -quantum error estimations for various integral inequalities via ( α , m ) (\alpha ,m) -convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.

scholarly journals New Hermite Hadamard type inequalities for twice differentiable convex mappings via Green function and applications

2016 ◽  
Vol 2 (2) ◽  
pp. 107-118 ◽  
Author(s):  
Samet Erden ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Green Function ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Absolute Value ◽  
Convex Mappings ◽  
Trapezoidal Formula ◽  
Special Means ◽  
Second Derivatives ◽  
Type Integral

Abstract We derive some Hermite Hamamard type integral inequalities for functions whose second derivatives absolute value are convex. Some eror estimates for the trapezoidal formula are obtained. Finally, some natural applications to special means of real numbers are given

scholarly journals Some new Gauss-Jacobi and Hermite-Hadamard type inequalities concerning $(n+1)$-differentiable generalized $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convex mappings

2018 ◽  
Vol 49 (4) ◽  
pp. 317-337 ◽  
Author(s):  
Artion Kashuri ◽  
Rozana Liko ◽  
Silvestru Sever Dragomir
Keyword(s):  
Fractional Derivatives ◽  
Integral Inequalities ◽  
Auxiliary Result ◽  
Convex Mappings ◽  
New Class ◽  
Special Cases ◽  
Type Integral

In this article, we first introduced a new class of generalized $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convex mappings and two interesting lemmas regarding Gauss-Jacobi and\\ Hermite-Hadamard type integral inequalities. By using the notion of generalized\\ $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convexity and the first lemma as an auxiliary result, some new estimates with respect to Gauss-Jacobi type integral inequalities are established. Also, using the second lemma, some new estimates with respect to Hermite-Hadamard type integral inequalities via Caputo $k$-fractional derivatives are obtained. It is pointed out that some new special cases can be deduced from main results of the article.

scholarly journals Some Parameterized Quantum Simpson’s and Quantum Newton’s Integral Inequalities via Quantum Differentiable Convex Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Xue Xiao You ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Miguel Vivas-Cortez ◽  
Shahid Qaisar
Keyword(s):  
Integral Inequalities ◽  
Riemann Integral ◽  
Convex Mappings ◽  
Quantum Integral ◽  
Special Cases ◽  
Newton’S Integral ◽  
Integral Identities

In this work, two generalized quantum integral identities are proved by using some parameters. By utilizing these equalities, we present several parameterized quantum inequalities for convex mappings. These quantum inequalities generalize many of the important inequalities that exist in the literature, such as quantum trapezoid inequalities, quantum Simpson’s inequalities, and quantum Newton’s inequalities. We also give some new midpoint-type inequalities as special cases. The results in this work naturally generalize the results for the Riemann integral.

scholarly journals Fractional Integral Inequalities for Differentiable Convex Mappings and Applications to Special Means and a Midpoint Formula

2012 ◽  
Vol 8 (2) ◽  
pp. 21-28 ◽  
Author(s):  
Chun Zhu ◽  
Michal Fečkan ◽  
Jinrong Wang
Keyword(s):  
Error Estimates ◽  
Integral Identity ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Liouville Type ◽  
Convex Mappings ◽  
Special Means

Abstract In this paper, Riemann-Liouville type fractional integral identity and inequality for differentiable convex mappings are studied. Some applications to special means of real numbers are given. Finally, error estimates for a midpoint formula are also obtained.

scholarly journals Fractional integral inequalities for generalized-$$\mathbf{m }$$-$$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$-convex mappings via an extended generalized Mittag–Leffler function

2019 ◽  
Vol 9 (2) ◽  
pp. 231-243
Author(s):  
George Anastassiou ◽  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Convex Mappings ◽  
Invex Set ◽  
Special Means ◽  
Special Cases

AbstractThe authors discover a new identity concerning differentiable mappings defined on $$\mathbf{m }$$ m -invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized-$$\mathbf{m }$$ m -$$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings by involving an extended generalized Mittag–Leffler function are presented. It is pointed out that some new special cases can be deduced from main results. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

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