scholarly journals NEW INEQUALITIES FOR LOCAL FRACTIONAL INTEGRALS PERTAINING GENERALIZED STRONGLY CONVEX MAPPINGS

2020 ◽  
pp. 91-106
Author(s):  
Artion Kashuri
Keyword(s):  
Fractional Integrals ◽  
Convex Mappings ◽  
Strongly Convex ◽  
New Inequalities

scholarly journals New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Saad Ihsan Butt ◽  
Saba Yousaf ◽  
Atifa Asghar ◽  
Khuram Ali Khan ◽  
Hamid Reza Moradi
Keyword(s):  
Convex Function ◽  
Hypergeometric Functions ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Convex Mappings ◽  
Special Means ◽  
Interesting Variation ◽  
Harmonically Convex Function ◽  
The Right ◽  
New Inequalities

In 2003, Mercer presented an interesting variation of Jensen’s inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard inequalities of the Jensen–Mercer type via fractional integrals. As a result, we introduce several related fractional inequalities connected with the right and left differences of obtained new inequalities for differentiable harmonically convex mappings. As an application viewpoint, new estimates regarding hypergeometric functions and special means of real numbers are exemplified to determine the pertinence and validity of the suggested scheme. Our results presented here provide extensions of others given in the literature. The results proved in this paper may stimulate further research in this fascinating area.

scholarly journals Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

scholarly journals New inequalities of Opial type for conformable fractional integrals

2017 ◽  
Vol 41 ◽  
pp. 1164-1173 ◽  
Author(s):  
Mehmet Zeki SARIKAYA ◽  
Hüseyin BUDAK
Keyword(s):  
Fractional Integrals ◽  
New Inequalities

scholarly journals Fractional Ostrowski type inequalities for differentiable harmonically convex functions

2021 ◽  
Vol 7 (3) ◽  
pp. 3939-3958
Author(s):  
Thanin Sitthiwirattham ◽  
◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Sotiris K. Ntouyas ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Special Means ◽  
Special Cases ◽  
Harmonically Convex Functions ◽  
New Inequalities

<abstract><p>In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and $ k $-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.</p></abstract>

scholarly journals Some New Tempered Fractional Pólya-Szegö and Chebyshev-Type Inequalities with Respect to Another Function

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Gauhar Rahman ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad ◽  
Muhammad Samraiz
Keyword(s):  
Present Article ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Bounded Functions ◽  
New Inequalities

In this present article, we establish certain new Pólya–Szegö-type tempered fractional integral inequalities by considering the generalized tempered fractional integral concerning another function Ψ in the kernel. We then prove certain new Chebyshev-type tempered fractional integral inequalities for the said operator with the help of newly established Pólya–Szegö-type tempered fractional integral inequalities. Also, some new particular cases in the sense of classical tempered fractional integrals are discussed. Additionally, examples of constructing bounded functions are considered. Furthermore, one can easily form new inequalities for Katugampola fractional integrals, generalized Riemann–Liouville fractional integral concerning another function Ψ in the kernel, and generalized fractional conformable integral by applying different conditions.

scholarly journals On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Qi Li ◽  
Muhammad Shoaib Saleem ◽  
Peiyu Yan ◽  
Muhammad Sajid Zahoor ◽  
Muhammad Imran
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Convex Functions ◽  
Fractional Integral ◽  
Optimization Problems ◽  
Fractional Integral Operator ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Special Means ◽  
New Inequalities

The theory of convex functions plays an important role in the study of optimization problems. The fractional calculus has been found the best to model physical and engineering processes. The aim of this paper is to study some properties of strongly convex functions via the Caputo–Fabrizio fractional integral operator. In this paper, we present Hermite–Hadamard-type inequalities for strongly convex functions via the Caputo–Fabrizio fractional integral operator. Some new inequalities of strongly convex functions involving the Caputo–Fabrizio fractional integral operator are also presented. Moreover, we present some applications of the proposed inequalities to special means.

scholarly journals On Hermite-Hadamard Type Inequalities for s–Convex Mappings via Fractional Integrals of a Function with Respect to Another Function

2016 ◽  
Vol 57 (1) ◽  
pp. 25-36 ◽  
Author(s):  
Hüseyin Budak ◽  
Mehmet Z. Sarikaya
Keyword(s):  
Convex Function ◽  
Fractional Integrals ◽  
Convex Mappings ◽  
Hadamard Fractional Integrals

AbstractIn this paper, we obtain some Hermite-Hadamard type inequalities fors–convex function via fractional integrals with respect to another function which generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. The results presented here provide extensions of those given in earlier works.

scholarly journals Fractional Versions of Hadamard-Type Inequalities for Strongly Exponentially α , h − m -Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Shasha Li ◽  
Ghulam Farid ◽  
Atiq Ur Rehman ◽  
Hafsa Yasmeen
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Strongly Convex ◽  
Error Estimations ◽  
Integral Identities

In this article, we prove some fractional versions of Hadamard-type inequalities for strongly exponentially α , h − m -convex functions via generalized Riemann–Liouville fractional integrals. The outcomes of this paper provide inequalities of strongly convex, strongly m -convex, strongly s -convex, strongly α , m -convex, strongly s , m -convex, strongly h − m -convex, strongly α , h − m -convex, strongly exponentially convex, strongly exponentially m -convex, strongly exponentially s -convex, strongly exponentially s , m -convex, strongly exponentially h − m -convex, and exponentially α , h − m -convex functions. The error estimations are also studied by applying two fractional integral identities.

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