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 On Extended General Mittag–Leffler Functions and Certain Inequalities

2019 ◽  
Vol 3 (2) ◽  
pp. 32
Author(s):  
Marcela V. Mihai ◽  
Muhammad Uzair Awan ◽  
Muhammad Aslam Noor ◽  
Tingsong Du ◽  
Artion Kashuri ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Function Of Two Variables ◽  
Generalized Fractional Integral Operators

In this paper, we introduce and investigate generalized fractional integral operators containing the new generalized Mittag–Leffler function of two variables. We establish several new refinements of Hermite–Hadamard-like inequalities via co-ordinated convex functions.

scholarly journals Fractional Hadamard and Fejér-Hadamard Inequalities Associated with Exponentially s,m-Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Shuya Guo ◽  
Yu-Ming Chu ◽  
Ghulam Farid ◽  
Sajid Mehmood ◽  
Waqas Nazeer
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Monotone Function ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

The aim of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities for exponentially s,m-convex functions. To establish these inequalities, we will utilize generalized fractional integral operators containing the Mittag-Leffler function in their kernels via a monotone function. The presented results in particular contain a number of fractional Hadamard and Fejér-Hadamard inequalities for s-convex, m-convex, s,m-convex, exponentially convex, exponentially s-convex, and convex functions.

scholarly journals On Some Generalized Fractional Integral Inequalities for p-Convex Functions

2019 ◽  
Vol 3 (2) ◽  
pp. 29
Author(s):  
Seren Salaş ◽  
Yeter Erdaş ◽  
Tekin Toplu ◽  
Erhan Set
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Hadamard Inequality ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

In this paper, firstly we have established a new generalization of Hermite–Hadamard inequality via p-convex function and fractional integral operators which generalize the Riemann–Liouville fractional integral operators introduced by Raina, Lun and Agarwal. Secondly, we proved a new identity involving this generalized fractional integral operators. Then, by using this identity, a new generalization of Hermite–Hadamard type inequalities for fractional integral are obtained.

scholarly journals Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Chahn Yong Jung ◽  
Muhammad Yussouf ◽  
Yu-Ming Chu ◽  
Ghulam Farid ◽  
Shin Min Kang
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Harmonically Convex Functions ◽  
Hadamard Fractional Integral ◽  
Generalized Fractional Integral Operators

In this paper, we define a new function, namely, harmonically α , h − m -convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejér–Hadamard fractional integral inequalities for harmonically α , h − m -convex functions via generalized fractional integral operators are proved. From presented results, a series of fractional integral inequalities can be obtained for harmonically convex, harmonically h − m -convex, harmonically α , m -convex, and related functions and for already known fractional integral operators.

scholarly journals Certain Inequalities Pertaining to Some New Generalized Fractional Integral Operators

2021 ◽  
Vol 5 (4) ◽  
pp. 160
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Kamsing Nonlaopon
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
Chebyshev Functional ◽  
Generalized Fractional Integral ◽  
Finite Products ◽  
Generalized Fractional Integral Operators

In this paper, we introduce the generalized left-side and right-side fractional integral operators with a certain modified ML kernel. We investigate the Chebyshev inequality via this general family of fractional integral operators. Moreover, we derive new results of this type of inequalities for finite products of functions. In addition, we establish an estimate for the Chebyshev functional by using the new fractional integral operators. From our above-mentioned results, we find similar inequalities for some specialized fractional integrals keeping some of the earlier results in view. Furthermore, two important results and some interesting consequences for convex functions in the framework of the defined class of generalized fractional integral operators are established. Finally, two basic examples demonstrated the significance of our results.

scholarly journals Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators

2016 ◽  
Vol 5 (1) ◽  
pp. 55-62
Author(s):  
Erhan Set ◽  
Abdurrahman Gözpinar
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Absolute Value ◽  
Type Integral ◽  
Generalized Fractional Integral ◽  
Fractional Type ◽  
Generalized Fractional Integral Operators

AbstractIn this present work, the authors establish a new integral identity involving generalized fractional integral operators and by using this fractional-type integral identity, obtain some new Hermite-Hadamard type inequalities for functions whose first derivatives in absolute value are convex. Relevant connections of the results presented here with those earlier ones are also pointed out.

scholarly journals New refinements of Chebyshev–Pólya–Szegö-type inequalities via generalized fractional integral operators

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Saad Ihsan Butt ◽  
Ahmet Ocak Akdemir ◽  
Muhammad Yousaf Bhatti ◽  
Muhammad Nadeem
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Inequality Theory ◽  
Synchronous Development ◽  
Fractional Analysis ◽  
Generalized Fractional Integral ◽  
Developing Area ◽  
Generalized Fractional Integral Operators ◽  
New Inequalities

Abstract Fractional analysis, as a rapidly developing area, is a tool to bring new derivatives and integrals into the literature with the effort put forward by many researchers in recent years. The theory of inequalities is a subject of many mathematicians’ work in the last century and has contributed to other areas with its applications. Especially in recent years, these two fields, fractional analysis and inequality theory, have shown a synchronous development. Inequality studies have been carried out by using new operators revealed in the fractional analysis. In this paper, by combining two important concepts of these two areas we obtain new inequalities of Chebyshev–Polya–Szegö type by means of generalized fractional integral operators. Our results are concerned with the integral of the product of two functions and the product of two integrals. They improve the results in the paper (J. Math. Inequal. 10(2):491–504, 2016).

scholarly journals New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 122
Author(s):  
Ahmet Ocak Akdemir ◽  
Saad Ihsan Butt ◽  
Muhammad Nadeem ◽  
Maria Alessandra Ragusa
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
Integrable Functions ◽  
Inequality Theory ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Chebyshev's Inequality ◽  
Generalized Fractional Integral Operators

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have generalized many existing results as well as iterating the Chebyshev inequality in special cases.

scholarly journals Some novel inequalities involving a function’s fractional integrals in relation to another function through generalized quasiconvex mappings

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3349-3360
Author(s):  
Eze Nwaeze ◽  
Artion Kashuri
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Absolute Value ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators ◽  
New Inequalities

In this paper, we establish new inequalities of the Hermite-Hadamard, midpoint and trapezoid types for functions whose first derivatives in absolute value are ?-quasiconvex by means of generalized fractional integral operators with respect to another function ? : [?,?] ? (0,?). Our theorems reduce to results involving the Riemann-Liouville fractional integral operators if ? is the identity map, and results involving the Hadamard operators if ?(x) = ln x. More inequalities can be deduced by choosing different bifunctions for ?. To the best of our knowledge, the results obtained herein are new and we hope that they will stimulate further interest in this direction.

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