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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
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A Note on Generalized Strongly p-Convex Functions of Higher Order

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2022
Generalized strongly -convex functions of higher order is a new concept of convex functions which introduced by Saleem et al. in 2020. The Schur type inequality for generalized strongly -convex functions of higher order also studied by them.
Corina Karim, Ekadion Maulana
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Quasi Semi and Pseudo Semi (p,E)-Convexity in Non-Linear Optimization Programming

Ibn Al-Haitham Journal for Pure and Applied Sciences, 2023
The class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively.
Revan I. Hazim, Saba N. Majeed
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Some Local Fractional Inequalities Involving Fractal Sets via Generalized Exponential (s,m)-Convexity

Axioms, 2023
Research in this paper aims to explore the concept of generalized exponentially (s,m)-convex functions, and to determine some properties of these functions.
Wedad Saleh, Adem Kılıçman
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Fractional Ostrowski-type Inequalities via $(\alpha,\beta,\gamma,\delta)-$convex Function [PDF]

Sahand Communications in Mathematical Analysis, 2023
In this paper, we are introducing for the first time a generalized class named the class of $(\alpha,\beta,\gamma,\delta)-$convex functions of mixed kind.
Ali Hassan, Asif R. Khan, Nazia Irshad, Sumbul Khatoon   +3 more
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Cauchy type means for some generalized convex functions

Journal of Inequalities and Applications, 2021
In this paper, we establish Jensen’s inequality for s-convex functions in the first sense. By using Jensen’s inequalities, we obtain some Cauchy type means for p-convex and s-convex functions in the first sense.
Naila Mehreen, Matloob Anwar
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Hermite–Hadamard-Type Inequalities for the Generalized Geometrically Strongly Modified h-Convex Functions

Journal of Mathematics, 2021
Convexity theory becomes a hot area of research due to its applications in pure and applied mathematics, especially in optimization theory. The aim of this paper is to introduce a broader class of convex functions by unifying geometrically strong convex ...
Xishan Yu, Muhammad Shoaib Saleem, Shumaila Waheed, Ilyas Khan   +3 more
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An equivalent condition to the Jensen inequality for the generalized Sugeno integral. [PDF]

, 2017
For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral.
Abbaszadeh, Sadegh, de la Sen, Manuel, Ebadian, Ali, Jaddi, Mohsen   +3 more
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Generalized geometrically convex functions and inequalities

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
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Geometric convexity of the generalized sine and the generalized hyperbolic sine [PDF]

, 2013
In the paper, the authors prove that the generalized sine function $\sin_{p,q}(x)$ and the generalized hyperbolic sine function $\sinh_{p,q}(x)$ are geometrically concave and geometrically convex, respectively.
Jiang, Wei-Dong, Qi, Feng
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