Results 1 to 10 of about 184,033 (233)

Some New Harmonically Convex Function Type Generalized Fractional Integral Inequalities

Fractal and Fractional, 2021
In this article, we established a new version of generalized fractional Hadamard and Fejér–Hadamard type integral inequalities. A fractional integral operator (FIO) with a non-singular function (multi-index Bessel function) as its kernel and monotone ...
Rana Safdar Ali, Aiman Mukheimer, Thabet Abdeljawad, Shahid Mubeen, Sabila Ali, Gauhar Rahman, Kottakkaran Sooppy Nisar   +6 more
doaj   +4 more sources

Novel extensions of k-harmonically convex functions and their applications in information science. [PDF]

PLoS ONE
Convex analysis theory has found extensive applications in optimization, information science, and economics, leading to numerous generalizations of convex functions.
Asfand Fahad, Shigeru Furuichi, Zammad Ali, Yuanheng Wang   +3 more
doaj   +3 more sources

Fractional Hermite-Hadamard inequalities containing generalized Mittag-Leffler function [PDF]

Journal of Inequalities and Applications, 2017
The objective of this paper is to establish some new refinements of fractional Hermite-Hadamard inequalities via a harmonically convex function with a kernel containing the generalized Mittag-Leffler function.
Marcela V Mihai, Muhammad Uzair Awan, Muhammad Aslam Noor, Khalida Inayat Noor   +3 more
doaj   +3 more sources

Hermite–Hadamard-Type Inequalities for Harmonically Convex Functions via Proportional Caputo-Hybrid Operators with Applications

Fractal and Fractional
In this paper, we aim to establish new inequalities of Hermite–Hadamard (H.H) type for harmonically convex functions using proportional Caputo-Hybrid (P.C.H) fractional operators.
Saad Ihsan Butt, Muhammad Umar, Dawood Khan, Youngsoo Seol, Sanja Tipurić-Spužević   +4 more
doaj   +4 more sources

Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities

International Journal of Computational Intelligence Systems, 2021
It is well known that the concept of convexity establishes strong relationship with integral inequality for single-valued and interval-valued function.
Gul Sana, Muhammad Bilal Khan, Muhammad Aslam Noor, Pshtiwan Othman Mohammed, Yu-Ming Chu   +4 more
doaj   +2 more sources

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

Journal of Function Spaces, 2021
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 ...
Saad Ihsan Butt, Saba Yousaf, Atifa Asghar, Khuram Ali Khan, Hamid Reza Moradi   +4 more
doaj   +2 more sources

The Properties of Harmonically cr-h-Convex Function and Its Applications

Mathematics, 2022
In this paper, the definition of the harmonically cr-h-convex function is given, and its important properties are discussed. Jensen type inequality, Hermite–Hadamard type inequalities and Fejér type inequalities for harmonically cr-h-convex functions are
Wei Liu, Fangfang Shi, Guoju Ye, Dafang Zhao   +3 more
doaj   +2 more sources

Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications

Journal of Inequalities and Applications, 2022
In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained.
Saad Ihsan Butt, Praveen Agarwal, Saba Yousaf, Juan L. G. Guirao   +3 more
doaj   +2 more sources

New generalized fractional versions of Hadamard and Fejér inequalities for harmonically convex functions

Journal of Inequalities and Applications, 2020
The aim of this paper is to establish new generalized fractional versions of the Hadamard and the Fejér–Hadamard integral inequalities for harmonically convex functions.
Xiaoli Qiang, Ghulam Farid, Muhammad Yussouf, Khuram Ali Khan, Atiq Ur Rahman   +4 more
doaj   +3 more sources

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

Journal of Mathematics, 2020
In this paper, we define a new function, namely, harmonically α,h−m-convex function, which unifies various kinds of harmonically convex functions.
Chahn Yong Jung, Muhammad Yussouf, Yu-Ming Chu, Ghulam Farid, Shin Min Kang   +4 more
doaj   +2 more sources