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Generalized Alpha-Close-to-Convex Functions [PDF]

International Journal of Mathematics and Mathematical Sciences, 2009
We define the classes Gβ(α,k,γ) as follows: f∈Gβ(α,k,γ) if and only if, for z∈E={z∈ℂ:|z|
K. Inayat Noor, Halit Orhan, Saima Mustafa   +2 more
doaj   +4 more sources

Generalized geometrically convex functions and inequalities [PDF]

Journal of Inequalities and Applications, 2017
In this paper, we introduce and study a new class of generalized functions, called generalized geometrically convex functions. We establish several basic inequalities related to generalized geometrically convex functions.
Muhammad Aslam Noor, Khalida Inayat Noor, Farhat Safdar   +2 more
doaj   +3 more sources

A note on generalized convex functions

Journal of Inequalities and Applications, 2019
In the article, we provide an example for a η-convex function defined on rectangle is not convex, prove that every η-convex function defined on rectangle is coordinate η-convex and its converse is not true in general, define the coordinate (η1,η2) $(\eta
Syed Zaheer Ullah, Muhammad Adil Khan, Yu-Ming Chu   +2 more
doaj   +3 more sources

Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications [PDF]

Mathematics, 2019
In the present paper, we investigate some Hermite-Hadamard ( HH ) inequalities related to generalized Riemann-Liouville fractional integral ( GRLFI ) via exponentially convex functions.
Saima Rashid, Thabet Abdeljawad, Fahd Jarad, Muhammad Aslam Noor   +3 more
openalex   +2 more sources

Generalized Legendre Transforms Have Roots in Information Geometry [PDF]

Entropy
Artstein-Avidan and Milman [Annals of mathematics (2009), (169):661–674] characterized invertible reverse-ordering transforms in the space of lower, semi-continuous, extended, real-valued convex functions as affine deformations of the ordinary Legendre ...
Frank Nielsen
doaj   +2 more sources

Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

Journal of Inequalities and Applications, 2021
In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals.
Xue-Xiao You, Muhammad Aamir Ali, Hüseyin Budak, Praveen Agarwal, Yu-Ming Chu   +4 more
doaj   +2 more sources

Integral inequalities via generalized convex functions

, 2017
. In this paper, we introduce the concept of generalized ( α , m ) -convex functions. Some new integral inequalities related to left hand side of the Hermite-Hadamard type for the class of functions whose second derivative at certain powers are ...
Muhammad Aslam Noor, Khalida Inayat Noor, Farhat Safdar   +2 more
openalex   +3 more sources

INEQUALITIES VIA GENERALIZED h-CONVEX FUNCTIONS

Проблемы анализа, 2018
In the paper, we establish some new Hermite-Hadamard-Fej´er type inequalities via generalized h-convex functions, Toader-like convex functions and their variant forms. Several special cases are also discussed. Results proved in this paper can be viewed
M. A. Noor, K. I. Noor, F. Safdar
doaj   +2 more sources

On Newton–Cotes Formula-Type Inequalities for Multiplicative Generalized Convex Functions via Riemann–Liouville Fractional Integrals with Applications to Quadrature Formulas and Computational Analysis

Fractal and Fractional
In this article, we develop multiplicative fractional versions of Simpson’s and Newton’s formula-type inequalities for differentiable generalized convex functions with the help of established identities.
Abdul Mateen, Serap Özcan, Zhiyue Zhang, Bandar Bin‐Mohsin   +3 more
openalex   +2 more sources

Some new local fractional inequalities associated with generalized ( s , m ) $(s,m)$ -convex functions and applications

Advances in Difference Equations, 2020
Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attractive field of research.
Thabet Abdeljawad, Saima Rashid, Zakia Hammouch, Yu-Ming Chu   +3 more
doaj   +2 more sources