scholarly journals The left conformable fractional Hermite-Hadamard type inequalities for convex functions

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2417-2430
Author(s):  
Sercan Turhan
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Conformable Fractional Integral

In this paper, a new fractional Hermite-Hadamard type inequality for convex functions is obtained by using only the left conformable fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved.

scholarly journals New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1753
Author(s):  
Saima Rashid ◽  
Aasma Khalid ◽  
Omar Bazighifan ◽  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Convex Mappings ◽  
Special Cases ◽  
Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

Conformable fractional integral inequalities for some convex functions

2018 ◽  
Vol 27 (2) ◽  
pp. 207-213
Author(s):  
ERHAN SET ◽  
◽  
BARIS CELIK ◽  
ABDURRAHMAN GOZPINAR ◽  
◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Conformable Fractional Integral

The main purpose of this paper is to present new Hermite-Hadamard’s type inequalities for functions that belongs to the classes of Q(I), P(I), SX(h, I) and r-convex via conformable fractional integrals . The results presented here would provide extensions of those given in earlier works

scholarly journals New Conformable Fractional Integral Inequalities of Hermite–Hadamard Type for Convex Functions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 263 ◽  
Author(s):  
Pshtiwan Mohammed ◽  
Faraidun Hamasalh
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Conformable Fractional Integral ◽  
New Inequalities

In this work, we established new inequalities of Hermite–Hadamard type for convex functions via conformable fractional integrals. Through the conformable fractional integral inequalities, we found some new inequalities of Hermite–Hadamard type for convex functions in the form of classical integrals.

Certain Hermite-Hadamard type inequalities associated with conformable fractional integral operators

2017 ◽  
Vol 26 (3) ◽  
pp. 321-330
Author(s):  
ERHAN SET ◽  
◽  
BARIS CELIK ◽  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Conformable Fractional Integral

The aim of this article is to obtain some new Hermite-Hadamard type inequalities for convex functions via conformable fractional integral. The results presented here would provide extensions of those given in earlier works.

scholarly journals Trapezium-Type Inequalities for k -Fractional Integral via New Exponential-Type Convexity and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Artion Kashuri ◽  
Sajid Iqbal ◽  
Saad Ihsan Butt ◽  
Jamshed Nasir ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Applied Sciences ◽  
Convex Function ◽  
Error Estimates ◽  
Exponential Type ◽  
Convex Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Trapezium Type ◽  
Special Means ◽  
Algebraic Properties

In this paper, the authors investigated the concept of s , m -exponential-type convex functions and their algebraic properties. New generalizations of Hermite–Hadamard-type inequality for the s , m -exponential-type convex function ψ and for the products of two s , m -exponential-type convex functions ψ and ϕ are proved. Many refinements of the (H–H) inequality via s , m -exponential-type convex are obtained. Finally, several new bounds for special means and new error estimates for the trapezoidal and midpoint formula are provided as well. The ideas and techniques of this paper may stimulate further research in different areas of pure and applied sciences.

scholarly journals New Conformable Fractional Integral Inequalities of Hermite-Hadamard Type for Convex Functions

2019 ◽  
Author(s):  
Pshtiwan Mohammed ◽  
Sever Dragomir
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Conformable Fractional Integral

In this work, we establish some new Hermite-Hadamard type inequalities for convex functions via conformable fractional integral. Moreover, we show that through the conformable fractional integral we can find some new Hermite-Hadamard type inequalities for convex functions via the classical integrals.

scholarly journals Fractional integral inequalities of Hermite-Hadamard type for convex functions with respect to a monotone function

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2401-2411
Author(s):  
Pshtiwan Mohammed
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Special Functions ◽  
Monotone Function ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Increasing Functions

In the literature, the left-side of Hermite-Hadamard?s inequality is called a midpoint type inequality. In this article, we obtain new integral inequalities of midpoint type for Riemann-Liouville fractional integrals of convex functions with respect to increasing functions. The resulting inequalities generalize some recent integral inequalities and Riemann-Liouville fractional integral inequalities established in earlier works. Finally, applications of our work are demonstrated via the known special functions.

scholarly journals Weighted Midpoint Hermite-Hadamard-Fejér Type Inequalities in Fractional Calculus for Harmonically Convex Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 252
Author(s):  
Humaira Kalsoom ◽  
Miguel Vivas-Cortez ◽  
Muhammad Amer Latif ◽  
Hijaz Ahmad
Keyword(s):  
Fractional Calculus ◽  
Convex Functions ◽  
Integral Identity ◽  
Fractional Integral ◽  
Symmetric Functions ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Type Integral ◽  
Harmonically Convex Functions

In this paper, we establish a new version of Hermite-Hadamard-Fejér type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Hadamard-Fejér type integral inequalities for harmonically convex functions by involving a positive weighted symmetric functions have been obtained. As shown, all of the resulting inequalities generalize several well-known inequalities, including classical and Riemann–Liouville fractional integral inequalities.

scholarly journals Midpoint Inequalities in Fractional Calculus Defined Using Positive Weighted Symmetry Function Kernels

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 550
Author(s):  
Pshtiwan Othman Mohammed ◽  
Hassen Aydi ◽  
Artion Kashuri ◽  
Y. S. Hamed ◽  
Khadijah M. Abualnaja
Keyword(s):  
Fractional Calculus ◽  
Weight Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Kernel ◽  
Type Inequality ◽  
Special Cases ◽  
Symmetry Function ◽  
Increasing Function

The aim of our study is to establish, for convex functions on an interval, a midpoint version of the fractional HHF type inequality. The corresponding fractional integral has a symmetric weight function composed with an increasing function as integral kernel. We also consider a midpoint identity and establish some related inequalities based on this identity. Some special cases can be considered from our main results. These results confirm the generality of our attempt.

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