Results 11 to 20 of about 282 (135)

A Generalization of Hermite–Hadamard–Fejer Type Inequalities for the p-Convex Function via α-Generator

Journal of Mathematics, 2023
In the 17th century, I. Newton and G. Leibniz found independently each other the basic operations of calculus, i.e., differentiation and integration. And this development broke new ground in mathematics.
Erdal Ünlüyol, Yeter Erdaş
doaj   +2 more sources

Advancements in Harmonic Convexity and Its Role in Modern Mathematical Analysis

Journal of Mathematics
Convex functions play an integral part in artificial intelligence by providing mathematical guarantees that make optimization more efficient and reliable.
Sabila Ali, Muhammad Samraiz, Saima Naheed, Miguel Vivas-Cortez   +3 more
doaj   +2 more sources

An Estimation of Different Kinds of Integral Inequalities for a Generalized Class of Godunova–Levin Convex and Preinvex Functions via Pseudo and Standard Order Relations

Journal of Function Spaces
The connection between generalized convexity and analytic operators is deeply rooted in functional analysis and operator theory. To put the ideas of preinvexity and convexity even closer together, we might state that preinvex functions are extensions of ...
Zareen A. Khan, Waqar Afzal
doaj   +2 more sources

A Generalized Version of Polynomial Convex Functions and Some Interesting Inequalities with Applications

Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023
In this article, we introduce a general class of convex functions and proved some of its basic properties. We establish Hermite‐Hadamard type inequalities as well as fractional version of Hermite‐Hadamard type inequalities by using Riemann‐Liouville integral operator. At the end, some application to special means of real numbers are also given.
Xiaogang Liu, Kiran Naseem Aslam, Muhammad Shoaib Saleem, Shuili Ren, Xuanlong Ma   +4 more
wiley   +1 more source

Some Hadamard–Fejér Type Inequalities for LR-Convex Interval-Valued Functions

Fractal and Fractional, 2021
The purpose of this study is to introduce the new class of Hermite–Hadamard inequality for LR-convex interval-valued functions known as LR-interval Hermite–Hadamard inequality, by means of pseudo-order relation ( ≤p ).
Muhammad Bilal Khan, Savin Treanțǎ, Mohamed S. Soliman, Kamsing Nonlaopon, Hatim Ghazi Zaini   +4 more
doaj   +1 more source

Some Interesting Inequalities for the Class of Generalized Convex Functions of Higher Order

Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023
In this paper, we study a generalized version of strongly reciprocally convex functions of higher order. Firstly, we prove some basic properties for addition, scalar multiplication, and composition of functions. Secondly, we establish Hermite‐Hadamard and Fejér type inequalities for the generalized version of strongly reciprocally convex functions of ...
Limei Liu, Muhammad Shoaib Saleem, Faisal Yasin, Kiran Naseem Aslam, Pengfei Wang, Mohsan Raza   +5 more
wiley   +1 more source

Jensen, Hermite–Hadamard, and Fejér‐Type Inequalities for Reciprocally Strongly (h, s)‐Convex Functions

Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023
This paper aims to present a generalized and extended notation of convexity by unifying reciprocally strong convexity with (h, s)−convexity. We introduce the concept of reciprocally strongly (h, s)−convex functions and establish some of their fundamental properties. In addition, we establish various inequalities, including Jensen, Hermite–Hadamard, and
Yujun Wang, Muhammad Shoaib Saleem, Zahida Perveen, Muhammad Imran, Firdous A. Shah   +4 more
wiley   +1 more source

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

Some New Hermite–Hadamard Type Inequalities Pertaining to Generalized Multiplicative Fractional Integrals [PDF]

, 2023
There is significant interaction between the class of symmetric functions and other types of functions. The multiplicative convex function class, which is intimately related to the idea of symmetry, is one of them.
Aljuaid, Munirah, De la Sen Parte, Manuel, Kashuri, Artion, Sahoo, Soubhagya Kumar, Tariq, Muhammad   +4 more
core   +1 more source

New Fractional Inequalities through Convex Functions and Comprehensive Riemann–Liouville Integrals

Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023
In most fields of applied sciences, inequalities are important in constructing mathematical systems and associated solution functions. Convexity also has a significant impact on an assortment of mathematical topics. By utilizing a comprehensive version of Riemann–Liouville integrals and the functions’ convexity condition, we present and prove novel ...
Abd-Allah Hyder, Çetin Yildiz
wiley   +1 more source