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 Trapezium-Type Inequalities for an Extension of Riemann–Liouville Fractional Integrals Using Raina’s Special Function and Generalized Coordinate Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 117
Author(s):  
Miguel Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge Eliecer Hernández Hernández
Keyword(s):  
Convex Functions ◽  
Special Function ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Several Variables ◽  
Special Cases ◽  
Interesting Identity ◽  
Generalized Coordinate

In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite–Hadamard inequality for generalized coordinate ϕ-convex functions via an extension of the Riemann–Liouville fractional integral. Furthermore, an interesting identity for functions with two variables is obtained, and with the use of it, some new extensions of trapezium-type inequalities using Raina’s special function via generalized coordinate ϕ-convex functions are developed. Various special cases have been studied. At the end, a brief conclusion is given as well.

scholarly journals Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández
Keyword(s):  
Hypergeometric Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Quantum Calculation ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Quantum Integral

In this work, a study is conducted on the Hermite–Hadamard inequality using a class of generalized convex functions that involves a generalized and parametrized class of special functions within the framework of quantum calculation. Similar results can be obtained from the results found for functions such as the hypergeometric function and the classical Mittag–Leffler function. The method used to obtain the results is classic in the study of quantum integral inequalities.

scholarly journals Hermite-Hadamard type inequalities for generalized convex functions on fractal sets style

2018 ◽  
Vol 38 (1) ◽  
pp. 101-116 ◽  
Author(s):  
Muharrem Tomar ◽  
Praveen Agarwal ◽  
Junesang Choi
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Generalized Convex Functions ◽  
Fractal Sets ◽  
Special Cases ◽  
Logarithmic Means ◽  
Local Fractional Integral ◽  
Generalized Arithmetic

We aim to  establish certain generalized Hermite-Hadamard's inequalities for generalized convex functions via local fractional integral. As special cases of some of the results presented here, certain interesting inequalities involving generalized arithmetic and logarithmic means are obtained.

scholarly journals Generalized Hadamard Fractional Integral Inequalities for Strongly s , m -Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Chao Miao ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Yanhua Bian
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Hadamard Fractional Integral

This article deals with Hadamard inequalities for strongly s , m -convex functions using generalized Riemann–Liouville fractional integrals. Several generalized fractional versions of the Hadamard inequality are presented; we also provide refinements of many known results which have been published in recent years.

scholarly journals On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity

2022 ◽  
Vol 6 (1) ◽  
pp. 28
Author(s):  
Tao Yan ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Chahn Yong Jung
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Generalized Convexity ◽  
Monotone Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Hadamard Inequality

In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann–Liouville fractional integrals. In this article, we define (α,h−m)-convex function with respect to a strictly monotone function that unifies several types of convexities defined in recent past. We establish fractional integral inequalities for this generalized convexity via Riemann–Liouville fractional integrals. The outcomes of this work contain compact formulas for fractional integral inequalities which generate results for different kinds of convex functions.

scholarly journals Some new inequalities for generalized convex functions pertaining generalized fractional integral operators and their applications

2021 ◽  
Vol 17 (1) ◽  
pp. 37-64
Author(s):  
A. Kashuri ◽  
M.A. Ali ◽  
M. Abbas ◽  
M. Toseef
Keyword(s):  
Differentiable Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Generalized Convex Functions ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators ◽  
New Inequalities

Abstract In this paper, authors establish a new identity for a differentiable function using generic integral operators. By applying it, some new integral inequalities of trapezium, Ostrowski and Simpson type are obtained. Moreover, several special cases have been studied in detail. Finally, many useful applications have been found.

scholarly journals Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 534
Author(s):  
Fangfang Shi ◽  
Guoju Ye ◽  
Dafang Zhao ◽  
Wei Liu
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Liouville Type ◽  
Special Cases ◽  
The Relationship ◽  
Interval Valued

In this paper, firstly we prove the relationship between interval h-convex functions and interval harmonically h-convex functions. Secondly, several new Hermite–Hadamard type inequalities for interval h-convex functions via interval Riemann–Liouville type fractional integrals are established. Finally, we obtain some new fractional Hadamard–Hermite type inequalities for interval harmonically h-convex functions by using the above relationship. Also we discuss the importance of our results and some special cases. Our results extend and improve some previously known results.

scholarly journals A Generalized Fejér-Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results

2018 ◽  
Author(s):  
Shin Min Kang ◽  
Ghulam Abbas ◽  
Ghulam Farid ◽  
Waqas Nazeer
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Hadamard Inequality ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Harmonically Convex Functions

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

scholarly journals Hermite-Hadamard type inequalities for p-convex functions via fractional integrals

2017 ◽  
Vol 3 (1) ◽  
pp. 22-34 ◽  
Author(s):  
Mehmet Kunt ◽  
İmdat İşcan
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Integral Forms ◽  
Type Integral ◽  
Integral Equality

Abstract In this paper, we present Hermite-Hadamard inequality for p-convex functions in fractional integral forms. we obtain an integral equality and some Hermite-Hadamard type integral inequalities for p-convex functions in fractional integral forms. We give some Hermite-Hadamard type inequalities for convex, harmonically convex and p-convex functions. Some results presented in this paper for p-convex functions, provide extensions of others given in earlier works for convex, harmonically convex and p-convex functions.

scholarly journals New trapezium type inequalities of coordinated distance-disturbed convex type functions of higher orders via extended Katugampola fractional integrals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Artion Kashuri ◽  
Sajid Iqbal ◽  
Rozana Liko ◽  
Muhammad Samraiz ◽  
Thabet Abdeljawad
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Trapezium Type ◽  
Special Cases ◽  
Sigma 1

AbstractIn this paper we establish some new results on trapezium type inequalities of coordinated distance-disturbed $(\ell _{1},h_{1})$ ( ℓ 1 , h 1 ) –$(\ell _{2},h_{2})$ ( ℓ 2 , h 2 ) -convex functions of higher orders $(\sigma _{1},\sigma _{2})$ ( σ 1 , σ 2 ) by using the Katugampola $(k_{1},k_{2})$ ( k 1 , k 2 ) -fractional integrals. As special cases of our general results, we recapture some earlier proved results.

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