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 New Simpson Type Integral Inequalities for s -Convex Functions and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Faraidun Hamasalh ◽  
Yuming Chu
Keyword(s):  
Error Estimation ◽  
Convex Functions ◽  
Bessel Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Theoretical Results

First, we consider a new Simpson’s identity. This identity investigates our main results that consist of some integral inequalities of Simpson’s type for the s –convex functions. From our main results, we obtain some special cases which are discussed in detail. Finally, some applications on the Bessel functions, special means of distinct positive real numbers, and error estimation about Simpson quadrature formula are presented to support our theoretical results.

scholarly journals On Some New Hermite-Hadamard Type Inequalities fors-Geometrically Convex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
İmdat İşcan
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means

Some new integral inequalities of Hermite-Hadamard type related to thes-geometrically convex functions are established and some applications to special means of positive real numbers are also given.

scholarly journals Some new generalized $ \kappa $–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications

2021 ◽  
Vol 7 (2) ◽  
pp. 3203-3220
Author(s):  
Miguel Vivas-Cortez ◽  
◽  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Artion Kashuri ◽  
...  
Keyword(s):  
Quadrature Formula ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Error Estimations ◽  
Integral Identities

<abstract><p>In this paper, we have established some new Hermite–Hadamard–Mercer type of inequalities by using $ {\kappa} $–Riemann–Liouville fractional integrals. Moreover, we have derived two new integral identities as auxiliary results. From the applied identities as auxiliary results, we have obtained some new variants of Hermite–Hadamard–Mercer type via $ {\kappa} $–Riemann–Liouville fractional integrals. Several special cases are deduced in detail and some know results are recaptured as well. In order to illustrate the efficiency of our main results, some applications regarding special means of positive real numbers and error estimations for the trapezoidal quadrature formula are provided as well.</p></abstract>

scholarly journals Some new bounds оf Gauss – Jacobi аnd Hermite – Hadamard type integral inequalities

2021 ◽  
Vol 73 (8) ◽  
pp. 1067-1084
Author(s):  
A. Kashuri ◽  
M. Ramosaçaj ◽  
R. Liko
Keyword(s):  
Error Estimates ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Type Integral

UDC 517.5 In this paper, authors discover two interesting identities regarding Gauss–Jacobi and Hermite–Hadamard type integral inequalities. By using the first lemma as an auxiliary result, some new bounds 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 general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from main results. Some applications to special means for different positive real numbers and new error estimates for the trapezoidal are provided as well. These results give us the generalizations, refinement and significant improvements of the new and previous known results. The ideas and techniques of this paper may stimulate further research.

scholarly journals New Inequalities of Fejer´ and Hermite-Hadamard type Concerning Convex and QuasiConvex Functions With Applications

2021 ◽  
pp. 83-99
Author(s):  
Muhammad Amer Latif ◽  
Sever Silvestru Dragomir ◽  
Sofian Obeidat
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Quasiconvex Functions ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
New Inequalities

This research contains new integral inequalities of Fejer and ´ Hermite-Hadamard type involving convex and quasi-convex functions. Applications of the newly established results for special means of positive real numbers are given.

scholarly journals New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Artion Kashuri ◽  
Kottakkaran Sooppy Nisar ◽  
Muhammad Zakria Javed ◽  
Sabah Iftikhar ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Quadrature Formulas ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Error Estimations ◽  
Harmonic Convex ◽  
Integral Identities

AbstractIn this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained.

Some new fractional integral inequalities for generalized relative semi-m-(r; h1, h2)-preinvex mappings via generalized Mittag-Leffler function

2019 ◽  
Vol 26 (1/2) ◽  
pp. 41-55 ◽  
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Invex Set ◽  
Special Means ◽  
Special Cases ◽  
Differentiable Mappings

The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. 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.

scholarly journals Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Bo-Yan Xi ◽  
Feng Qi
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Special Means ◽  
New Inequalities

The authors establish some new inequalities for differentiable convex functions, which are similar to the celebrated Hermite-Hadamard's integral inequality for convex functions, and apply these inequalities to construct inequalities for special means of two positive numbers.

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).

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