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We present a Carlson type inequality for the generalized Sugeno integral and a much wider class of functions than the comonotone functions. We also provide three Carlson type inequalities for the Choquet integral. Our inequalities…

Functional Analysis · Mathematics 2015-02-25 Michał Boczek , Marek Kaluszka

Let $\left( p,q\right) \mapsto \beta \left( p,q\right) $ be a function defined on $\mathbb{R}^{2}$. We determine the best or better $p,q$ such that the inequality% \begin{equation*} \left( \frac{\sin x}{x}\right) ^{p}<\left( >\right)…

Classical Analysis and ODEs · Mathematics 2014-08-12 Zhen-Hang Yang

In the paper, we introduce the generalized convex function on fractal sets of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen inequality and…

Classical Analysis and ODEs · Mathematics 2014-06-30 Huixia Mo , Xin Sui , Dongyan Yu

This article is devoted to the sharp improvement of the classical Bohr inequality for bounded analytic functions defined on the unit disk. We also prove two other sharp versions of the Bohr inequality by replacing the constant term by the…

Complex Variables · Mathematics 2020-04-21 Amir Ismagilov , Ilgiz R Kayumov , Saminathan Ponnusamy

We present a generalization of Schlick's bias and gain functions -- simple parametric curve-shaped functions for inputs in [0, 1]. Our single function includes both bias and gain as special cases, and is able to describe other smooth and…

Graphics · Computer Science 2020-10-21 Jonathan T. Barron

In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.

Complex Variables · Mathematics 2021-04-15 Saminathan Ponnusamy , Ramakrishnan Vijayakumar

In this paper, we give the refinement of an extension of Jensen's inequality to affine combinations. Furthermore, we present the functional form of Jensen's inequality for continuous 3-convex functions of one variable at a point.

Classical Analysis and ODEs · Mathematics 2016-01-25 Imran Abbas Baloch , Silvestru Sever Dragomir

A generalised trapezoid inequality for convex functions and applications for quadrature rules are given. A refinement and a counterpart result for the Hermite-Hadamard inequalities are obtained and some inequalities for pdf's and…

Numerical Analysis · Mathematics 2025-10-20 Sever Silvestru Dragomir

The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.

Classical Analysis and ODEs · Mathematics 2019-05-07 Hamid Reza Moradi , Shigeru Furuichi

We make a careful analysis of Bohr's inequality, in the line started by Kayumov and Ponnusamy, where some extra summand (depending on the function) is added in the right-hand side of the inequality. We analyse the inequality when smaller…

Complex Variables · Mathematics 2024-09-27 Mario Guillén , Pablo Sevilla-Peris

A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.

Classical Analysis and ODEs · Mathematics 2017-01-17 Iosif Pinelis

In this paper we deal with improvement of Jensen, Jensen-Steffensen's and Jensen's functionals related inequalities for uniformly convex, phi-convex and superquadratic functions.

Functional Analysis · Mathematics 2025-01-03 Shoshana Abramovich

In a recent work of the authors, we showed some general inequalities governing numerical radius inequalities using convex functions. In this article, we present results that complement the aforementioned inequalities. In particular, the new…

Functional Analysis · Mathematics 2019-07-10 Hamid Reza moradi , Mohammad Sababheh

In this paper, we investigate the monotonicity and inequalities for some functions involving the arc lemniscate and the hyperbolic arc lemniscate functions. In particular, sharp Shafer-Fink type inequalities for the arc lemniscate and the…

Classical Analysis and ODEs · Mathematics 2019-05-29 Minjie Wei , Yue He , Gendi Wang

Identities and inequalities for the cosine and sine functions are obtained.

Classical Analysis and ODEs · Mathematics 2020-01-13 Iosif Pinelis

We study $L^p$ inequalities that sharpen the triangle inequality for sums of $N$ functions in $L^p$.

Functional Analysis · Mathematics 2019-02-13 Eric A. Carlen , Rupert L. Frank , Elliott H. Lieb

In this article we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They…

Classical Analysis and ODEs · Mathematics 2020-11-24 Slavko Simic

In the paper $\lambda$-method Mitrinovic-Vasic is applied aiming to improve Fink's inequality, and Shafer's inequality for arcus sinus function is observed.

Classical Analysis and ODEs · Mathematics 2007-05-23 Branko J. Malesevic

In this paper, we present a refined version of the (classical) Stein inequality for the Fourier transform, elevating it to a new level of accuracy. Furthermore, we establish extended analogues of a more precise version of the Stein…

Functional Analysis · Mathematics 2024-11-19 Erlan D. Nursultanov , Durvudkhan Suragan

A crucial extension of quaternionic function theory to octonions is the concept of slice regular functions, introduced to handle holomorphic-like properties in a non-associative setting. In this paper, first we present a generalization of…

Complex Variables · Mathematics 2025-07-04 Sabir Ahammed , Molla Basir Ahamed