scholarly journals Hermite-Hadamard-Fejér Inequalities for Conformable Fractional Integrals via Preinvex Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Yousaf Khurshid ◽  
Muhammad Adil Khan ◽  
Yu-Ming Chu ◽  
Zareen Abdulhameed Khan
Keyword(s):  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Right Hand ◽  
Fejér Inequality ◽  
Preinvex Functions ◽  
The Right

In this paper, we present a Hermite-Hadamard-Fejér inequality for conformable fractional integrals by using symmetric preinvex functions. We also establish an identity associated with the right hand side of Hermite-Hadamard inequality for preinvex functions; then by using this identity and preinvexity of functions and some well-known inequalities, we find several new Hermite-Hadamard type inequalities for conformal fractional integrals.

scholarly journals Hermite-Hadamard-Fejér Type Inequalities for Preinvex Functions Using Fractional Integrals

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 467
Author(s):  
Sikander Mehmood ◽  
Fiza Zafar ◽  
Nusrat Yasmin
Keyword(s):  
Fractional Integrals ◽  
Weighted Estimates ◽  
Right Hand ◽  
Left And Right ◽  
Fejér Inequality ◽  
Preinvex Functions

In this paper, we have established the Hermite–Hadamard–Fejér inequality for fractional integrals involving preinvex functions. The results presented here provide new extensions of those given in earlier works as the weighted estimates of the left and right hand side of the Hermite–Hadamard inequalities for fractional integrals involving preinvex functions doesn’t exist previously.

scholarly journals Trapezium-Type Inequalities for Raina’s Fractional Integrals Operator Using Generalized Convex Functions

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1034 ◽  
Author(s):  
Miguel Vivas-Cortez ◽  
Artion Kashuri ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Special Functions ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Special Cases ◽  
The Right ◽  
The Relationship

The authors have reviewed a wide production of scientific articles dealing with the evolution of the concept of convexity and its various applications, and based on this they have detected the relationship that can be established between trapezoidal inequalities, generalized convex functions, and special functions, in particular with the so-called Raina function, which generalizes other better known ones such as the hypergeometric function and the Mittag–Leffler function. The authors approach this situation by studying the Hermite–Hadamard inequality, establishing a useful identity using Raina’s fractional integral operator in the setting of ϕ -convex functions, obtaining some integral inequalities connected with the right-hand side of Hermite–Hadamard-type inequalities for Raina’s fractional integrals. Various special cases have been identified.

scholarly journals On Hermite-Hadamard Type Inequalities fors-Convex Functions on the Coordinates via Riemann-Liouville Fractional Integrals

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Feixiang Chen
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Right Hand ◽  
The Right

We obtain some Hermite-Hadamard type inequalities fors-convex functions on the coordinates via Riemann-Liouville integrals. Some integral inequalities with the right-hand side of the fractional Hermite-Hadamard type inequality are also established.

scholarly journals Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
M. Rostamian Delavar ◽  
S. Mohammadi Aslani ◽  
M. De La Sen
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
Fejér Inequality ◽  
The Absolute

This paper deals with Hermite-Hadamard-Fejér inequality for (η1,η2)-convex functions via fractional integrals. Some mid-point and trapezoid type inequalities related to Hermite-Hadamard inequality when the absolute value of derivative of considered function is (η1,η2)-convex functions are obtained. Furthermore, a refinement for classic Hermite-Hadamard inequality via fractional integrals is given when a positive (η1,η2)-convex function is increasing.

scholarly journals ASYMPTOTIC INTEGRATION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRODIFFERENTIAL RIGHT-HAND SIDE

2015 ◽  
Vol 20 (4) ◽  
pp. 471-489 ◽  
Author(s):  
Milan Medved ◽  
Michal Pospisil
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Asymptotic Integration ◽  
Fractional Integrals ◽  
Left Hand ◽  
Right Hand ◽  
Fractional Differential ◽  
The Right ◽  
Derivatives Of ◽  
Fractional Orders

In this paper we deal with the problem of asymptotic integration of a class of fractional differential equations of the Caputo type. The left-hand side of such type of equation is the Caputo derivative of the fractional order r ∈ (n − 1, n) of the solution, and the right-hand side depends not only on ordinary derivatives up to order n − 1 but also on the Caputo derivatives of fractional orders 0 < r 1 < · · · < r m < r, and the Riemann–Liouville fractional integrals of positive orders. We give some conditions under which for any global solution x(t) of the equation, there is a constant c ∈ R such that x(t) = ctR + o(tR) as t → ∞, where R = max{n − 1, r m }.

Refinement of fejér inequality for convex and co-ordinated convex functions

2020 ◽  
Vol 70 (3) ◽  
pp. 585-598
Author(s):  
Kai-Chen Hsu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Beta Function ◽  
Right Hand ◽  
Fejér Inequality ◽  
The Right

AbstractIn this paper, we shall establish the co-ordinated convex function. It can connect to the right-hand side of Fejér inequality in two variables and thus a new refinement can be found. In addition, some applications to estimates for Euler’s Beta function are also given in the end.

scholarly journals Hermite–Hadamard-type inequalities for interval-valued preinvex functions via Riemann–Liouville fractional integrals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nidhi Sharma ◽  
Sanjeev Kumar Singh ◽  
Shashi Kant Mishra ◽  
Abdelouahed Hamdi
Keyword(s):  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Interval Valued Function ◽  
Preinvex Functions ◽  
Theoretical Results ◽  
Interval Valued

AbstractIn this paper, we introduce $(h_{1},h_{2})$ ( h 1 , h 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two interval-valued functions. Further, some examples are given to confirm our theoretical results.

Editorial Note

1946 ◽  
Vol 11 (1) ◽  
pp. 2-2
Keyword(s):  
Editorial Note ◽  
Speech Sounds ◽  
Left Hand ◽  
Hand Column ◽  
Right Hand ◽  
Infant Speech ◽  
The Right

In the article “Infant Speech Sounds and Intelligence” by Orvis C. Irwin and Han Piao Chen, in the December 1945 issue of the Journal, the paragraph which begins at the bottom of the left hand column on page 295 should have been placed immediately below the first paragraph at the top of the right hand column on page 296. To the authors we express our sincere apologies.

Sign in / Sign up

Export Citation Format

Share Document