scholarly journals New Integral Inequalities via Harmonically Convex Functions

2015 ◽  
Vol 3 (5) ◽  
pp. 134-140 ◽  
Author(s):  
Imdat Iscan ◽  
Mustafa Aydin ◽  
Sema Dikmenoglu
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Harmonically Convex Functions

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.

scholarly journals Hadamard and Fejér–Hadamard Inequalities for Further Generalized Fractional Integrals Involving Mittag-Leffler Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
M. Yussouf ◽  
G. Farid ◽  
K. A. Khan ◽  
Chahn Yong Jung
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Harmonically Convex Functions

In this paper, generalized versions of Hadamard and Fejér–Hadamard type fractional integral inequalities are obtained. By using generalized fractional integrals containing Mittag-Leffler functions, some well-known results for convex and harmonically convex functions are generalized. The results of this paper are connected with various published fractional integral inequalities.

scholarly journals Some integral inequalities for co-ordinated harmonically convex functions via fractional integrals

2020 ◽  
Vol 3 (4) ◽  
pp. 60-74
Author(s):  
Naila Mehreen ◽  
◽  
Matloob Anwar ◽  
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Harmonically Convex Functions

In this paper, we find some Hermite-Hadamard type inequalities for co-ordinated harmonically convex functions via fractional integrals.

Integral inequalities for coordinated Harmonically convex functions

2014 ◽  
Vol 60 (6) ◽  
pp. 776-786 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Muhammad Uzair Awan
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Harmonically Convex Functions

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 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 Novel Refinements via n –Polynomial Harmonically s –Type Convex Functions and Application in Special Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Saad Ihsan Butt ◽  
Saima Rashid ◽  
Muhammad Tariq ◽  
Miao-Kun Wang
Keyword(s):  
Convex Function ◽  
Hypergeometric Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Algebraic Properties ◽  
Type Integral ◽  
Harmonically Convex Functions ◽  
Formula Type

In this work, we introduce the idea of n –polynomial harmonically s –type convex function. We elaborate the new introduced idea by examples and some interesting algebraic properties. As a result, new Hermite–Hadamard, some refinements of Hermite–Hadamard and Ostrowski type integral inequalities are established, which are the generalized variants of the previously known results for harmonically convex functions. Finally, we illustrate the applicability of this new investigation in special functions (hypergeometric function and special mean of real numbers).

scholarly journals Trapezoidal Type Fejér Inequalities Related to Harmonically Convex Functions and Application

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Sercan Turhan
Keyword(s):  
Real Number ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Preliminary Results ◽  
Fejér Inequality ◽  
Harmonically Convex Functions

Some authors introduced the concepts of the harmonically arithmetic convex functions and establish some integral inequalities of Hermite Hadamard Fejér type related to the harmonically arithmetic convex functions. In this paper, a mapping M(t) is considered to get some preliminary results and a new trapezoidal form of Fejér inequality related to the harmonically arithmetic convex functions. By using a mapping M(t), the new theorems and corollaries are obtained. Taking advantage of these, applications were given for some real number averages.

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