Results 1 to 10 of about 245 (199)

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   +2 more sources

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   +3 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   +2 more sources

Hermite–Hadamard–Mercer-Type Inequalities for Harmonically Convex Mappings

Mathematics, 2021
In this paper, we prove Hermite–Hadamard–Mercer inequalities, which is a new version of the Hermite–Hadamard inequalities for harmonically convex functions.
Xuexiao You, Muhammad Aamir Ali, Hüseyin Budak, Jiraporn Reunsumrit, Thanin Sitthiwirattham   +4 more
doaj   +3 more sources

Hermite-Hadamard Inequalities in Fractional Calculus for Left and Right Harmonically Convex Functions via Interval-Valued Settings

Fractal and Fractional, 2022
The purpose of this study is to define a new class of harmonically convex functions, which is known as left and right harmonically convex interval-valued function (LR-𝓗-convex IV-F), and to establish novel inclusions for a newly defined class of interval-
Muhammad Bilal Khan, Jorge E. Macías-Díaz, Savin Treanțǎ, Mohammed S. Soliman, Hatim Ghazi Zaini   +4 more
doaj   +3 more sources

Generalized Harmonically Convex Fuzzy-Number-Valued Mappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities

Mathematics, 2023
We propose the concept of up and down harmonically convex mapping for fuzzy-number-valued mapping as our main goal in this work. With the help of up and down harmonically fuzzy-number convexity and the fuzzy fractional integral operator, we also show the
Muhammad Bilal Khan, Aleksandr Rakhmangulov, Najla Aloraini, Muhammad Aslam Noor, Mohamed S. Soliman   +4 more
doaj   +3 more sources

A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results

Mathematics, 2018
In this paper, we obtain a version of the Fejér–Hadamard inequality for harmonically convex functions via generalized fractional integral operator.
Shin Min Kang, Ghulam Abbas, Ghulam Farid, Waqas Nazeer   +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   +3 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   +1 more source

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   +1 more source