Hermite-Hadamard type local fractional integral inequalities with Mittag-Leffler kernel for generalized preinvex functions

Fractals ◽  
2021 ◽  
Author(s):  
Wenbing Sun
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Local Fractional Integral ◽  
Preinvex Functions

SOME LOCAL FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED PREINVEX FUNCTIONS AND APPLICATIONS TO NUMERICAL QUADRATURE

Fractals ◽  
2019 ◽  
Vol 27 (05) ◽  
pp. 1950071 ◽  
Author(s):  
WENBING SUN
Keyword(s):  
Numerical Integration ◽  
Error Estimates ◽  
Fractional Integral ◽  
Numerical Quadrature ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Parallel Development ◽  
Special Values ◽  
Local Fractional Integral ◽  
Preinvex Functions

In this paper, a new identity with parameters involving local fractional integrals is derived. Using this identity, some general local fractional integral inequalities for generalized preinvex functions are established. A parallel development is deduced for generalized preconcave functions. Taking special values for the parameters, some generalized midpoint inequalities, trapezoidal inequalities and Simpson inequalities are obtained. Finally, as some applications, error estimates of numerical integration for local fractional integrals are given.

scholarly journals Fractional trapezium-type inequalities for strongly exponentially generalized preinvex functions with applications

2020 ◽  
pp. 38-38
Author(s):  
Artion Kashuri ◽  
Themistocles Rassias
Keyword(s):  
Applied Sciences ◽  
Error Estimates ◽  
Quadrature Formula ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Trapezium Type ◽  
Type Integral ◽  
Preinvex Functions

The aim of this paper is to introduce a new extension of preinvexity called strongly exponentially generalized (m; !1; !2; h1; h2)-preinvexity. Some new integral inequalities of trapezium-type for strongly exponentially generalized (m; !1; !2; h1; h2)-preinvex functions with modulus c via Riemann-Liouville fractional integral are established. Also, some new estimates with respect to trapezium-type integral inequalities for strongly exponentially generalized (m; !1; !2; h1; h2)-preinvex functions with modulus c via general fractional integrals are obtained. We show that the class of strongly exponentially generalized (m; !1; !2; h1; h2)-preinvex functions with modulus c includes several other classes of preinvex functions. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.

scholarly journals Fractional integral identity, estimation of its bounds and some applications to trapezoidal quadrature rule

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2629-2641
Author(s):  
Artion Kashuri ◽  
Muhammad Awan ◽  
Muhammad Noor
Keyword(s):  
Applied Sciences ◽  
Integral Identity ◽  
Fractional Integral ◽  
Quadrature Rule ◽  
The Other ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Trapezium Type ◽  
Type Integral ◽  
Preinvex Functions

The aim of this paper is to introduce a new extension of preinvexity called exponentially (m,?1,?2, h1,h2)-preinvexity. Some new integral inequalities of Hermite-Hadamard type for exponentially (m,?1,?2,h1,h2)-preinvex functions via Riemann-Liouville fractional integral are established. Also, some new estimates with respect to trapezium-type integral inequalities for exponentially (m,?1,?2,h1,h2)-preinvex functions via general fractional integrals are obtained. We show that the class of exponentially (m,?1,?2, h1,h2)-preinvex functions includes several other classes of preinvex functions. We shown by two basic examples the efficiency of the obtained inequalities on the base of comparing those with the other corresponding existing ones. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.

scholarly journals ON SOME FRACTIONAL INTEGRAL INEQUALITIES OF HERMITE-HADAMARD TYPE FOR r-PREINVEX FUNCTIONS

2016 ◽  
Author(s):  
Abdullah AKKURT ◽  
Hüseyin YILDIRIM
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Preinvex Functions

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

Some new local fractional integral inequalities

2017 ◽  
Vol 10 (2) ◽  
pp. 133-143
Author(s):  
Mehmet Zeki Sarikaya ◽  
Hüseyin Budak
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Local Fractional Integral

scholarly journals A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Wei Wei ◽  
H. M. Srivastava ◽  
Yunyi Zhang ◽  
Lei Wang ◽  
Peiyi Shen ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Local Fractional Integral ◽  
Fractal Space ◽  
Integral Analogue

Anderson's inequality (Anderson, 1958) as well as its improved version given by Fink (2003) is known to provide interesting examples of integral inequalities. In this paper, we establish local fractional integral analogue of Anderson's inequality on fractal space under some suitable conditions. Moreover, we also show that the local fractional integral inequality on fractal space, which we have proved in this paper, is a new generalization of the classical Anderson's inequality.

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