scholarly journals k -Fractional Variants of Hermite-Mercer-Type Inequalities via s -Convexity with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Saad Ihsan Butt ◽  
Jamshed Nasir ◽  
Shahid Qaisar ◽  
Khadijah M. Abualnaja
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Special Functions ◽  
Integral Operators ◽  
The Novel ◽  
Differentiable Mapping ◽  
Real Numbers ◽  
Fractional Integral Operators ◽  
Special Means ◽  
The Absolute

This article is aimed at studying novel generalizations of Hermite-Mercer-type inequalities within the Riemann-Liouville k -fractional integral operators by employing s -convex functions. Two new auxiliary results are derived to govern the novel fractional variants of Hadamard-Mercer-type inequalities for differentiable mapping Ψ whose derivatives in the absolute values are convex. Moreover, the results also indicate new lemmas for Ψ ′ , Ψ ′ ′ , and Ψ ′ ′ ′ and new bounds for the Hadamard-Mercer-type inequalities via the well-known Hölder’s inequality. As an application viewpoint, certain estimates in respect of special functions and special means of real numbers are also illustrated to demonstrate the applicability and effectiveness of the suggested scheme.

scholarly journals New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Qiong Kang ◽  
Saad Ihsan Butt ◽  
Waqas Nazeer ◽  
Mehroz Nadeem ◽  
Jamshed Nasir ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Hölder’S Inequality ◽  
Integral Operators ◽  
Differentiable Mapping ◽  
Fractional Integral Operators ◽  
Hölder's Inequality ◽  
Differentiable Functions ◽  
New Variant ◽  
The Absolute

In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for differentiable mapping ϒ whose derivatives in the absolute values are convex. Moreover, we construct new lemmas for differentiable functions ϒ′, ϒ″, and ϒ‴ and formulate related inequalities for these differentiable functions using variants of Hölder’s inequality.

scholarly journals On generalization of Fejér type inequalities via fractional integral operators

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5537-5547 ◽  
Author(s):  
Erhan Set ◽  
Ahmet Akdemir ◽  
Barış Çelik
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Differentiable Mapping ◽  
Fractional Integral Operators

In this paper we first prove a new lemma for differentiable mapping via a fractional integral operator. Then, using lemma, we establish some new Hermite-Hadamard-Fejer type results for convex functions via fractional integral operators. The results presented here would provide extensions of those given in earlier works.

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 Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1225 ◽  
Author(s):  
Saima Rashid ◽  
Fahd Jarad ◽  
Muhammad Aslam Noor ◽  
Humaira Kalsoom ◽  
Yu-Ming Chu
Keyword(s):  
Real World ◽  
Fractional Integral ◽  
Numerical Approximation ◽  
Integral Operators ◽  
Integral Inequalities ◽  
The Novel ◽  
Fractional Integral Operators ◽  
Real World Problems

In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Ψ . The authors prove several inequalities for newly defined GPF-integral with respect to another function Ψ . Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Ψ and the proportionality index ς . Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.

scholarly journals Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities involving fractional integral operators

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2367-2380 ◽  
Author(s):  
Erhan Set ◽  
Ahmet Akdemir ◽  
Emrullah Alan
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Weighted Function ◽  
Fractional Integral Operators

Since the so-called Hermite-Hadamard type inequalities for convex functions were presented, their generalizations, refinements, and variants involving various integral operators have been extensively investigated. Here we aim to establish several Hermite-Hadamard inequalities and Hermite- Hadamard-Fejer type inequalities for symmetrized convex functions and Wright-quasi-convex functions with a weighted function symmetric with respect to the midpoint axis on the interval involving the fractional conformable integral operators initiated by Jarad et al. [9]. We also point out that certain known inequalities are particular cases of the results presented here.

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 Some Inequalities of Generalized p-Convex Functions concerning Raina’s Fractional Integral Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Changyue Chen ◽  
Muhammad Shoaib Sallem ◽  
Muhammad Sajid Zahoor
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Applied Mathematics ◽  
Optimization Theory ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Fractional Integral Operators

Convex functions play an important role in pure and applied mathematics specially in optimization theory. In this paper, we will deal with well-known class of convex functions named as generalized p-convex functions. We develop Hermite–Hadamard-type inequalities for this class of convex function via Raina’s fractional integral operator.

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