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This paper investigates the generalized convexity properties of the Lambert $W$ function, defined as the solution to $W(z)e^{W(z)}=z$. Focusing on $H_{p,q}$-convexity and concavity with respect to H\"older means, we derive necessary and…

Classical Analysis and ODEs · Mathematics 2025-08-26 Gendi Wang

In this paper, the author introduces the concept of the symmetrized p-convex function, gives Hermite-Hadamard type inequalities for symmetrized p-convex functions.

General Mathematics · Mathematics 2019-01-30 İmdat İşcan

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are P-functions. Some applications to special means of real…

Classical Analysis and ODEs · Mathematics 2014-05-01 Imdat Iscan , Erhan Set , M. Emin Ozdemir

A generalization of Powers-St$\o$rmer's inequality for operator monotone functions on $[0, +\infty)$ and for positive linear functional on general $C^*$-algebras will be proved. It also will be shown that the generalized Powers-St$\o$rmer…

Operator Algebras · Mathematics 2012-05-01 Dinh Trung Hoa , Hiroyuki Osaka , Ho Minh Toan

In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to…

Classical Analysis and ODEs · Mathematics 2014-06-30 Mevlut Tunc , Sevil Balgecti

We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the…

Convex functions have played a major role in the field of Mathematical inequalities. In this paper, we introduce a new concept related to convexity, which proves better estimates when the function is somehow more convex than another. In…

Functional Analysis · Mathematics 2020-03-25 M. Sababheh , S. Furuichi , H. R. Moradi

The paper studies logarithmic convexity and concavity of power series with coefficients involving q-gamma functions or q-shifted factorials with respect to a parameter contained in their arguments. The principal motivating examples of such…

Classical Analysis and ODEs · Mathematics 2017-02-14 S. I. Kalmykov , D. B. Karp

We quickly review and make some comments on the concept of convexity in metric spaces due to Takahashi. Then we introduce a concept of convex structure based convexity to functions on these spaces and refer to it as $W-$convexity.…

Functional Analysis · Mathematics 2015-09-01 Ahmed A. Abdelhakim

In this paper, a new identity for convex functions is derived. A consequence of the identity is that we can derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in…

Classical Analysis and ODEs · Mathematics 2012-07-31 Imdat Iscan

We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on this fact, an extension of the…

Classical Analysis and ODEs · Mathematics 2014-10-03 Constantin P. Niculescu , Ionel Roventa

The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional $p-$Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and…

Classical Analysis and ODEs · Mathematics 2013-09-20 Riku Klén , Matti Vuorinen , Xiaohui Zhang

This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral convexity under sums and compositions of multifunctions, the domains and ranges…

Optimization and Control · Mathematics 2023-10-19 Nguyen Ngoc Luan , Nguyen Mau Nam , Nguyen Dong Yen

In this paper our aim is to present the completely monotonicity and convexity properties for the Wright function. As consequences of these results, we present some functional inequalities. Moreover, we derive the monotonicity and…

Classical Analysis and ODEs · Mathematics 2017-08-03 Khaled Mehrez

In this paper, an integral identity for twice differentiable functions is generalized. Then, by using convexity of |f''| or q-th power of |f''| and with the aid of power mean and Holder's inequalities we achieved some new results. We also…

Functional Analysis · Mathematics 2015-03-10 Mustafa Gurbuz , Abdullah Yaradilmis

In this paper, we establish new general inequality for convex functions. Then we apply this inequality to obtain the midpoint, trapezoid and averaged midpoint-trapezoid integral inequality. Also, some applications for special means of real…

Classical Analysis and ODEs · Mathematics 2012-05-10 M. Z. Sarikaya , H. Ogunmez , M. K. Yildiz

In the present paper, we first prove the logarithmic convexity of the elementary function $\frac{b^x-a^x}x$, where $x\ne0$ and $b>a>0$. Basing on this, we then provide a simple proof for Schur-convex properties of the extended mean values,…

Classical Analysis and ODEs · Mathematics 2011-07-19 Feng Qi , Bai-Ni Guo

In this paper, the authors establish a new type integral inequalities for differentiable s-convex functions in the second sense. By the well-known H\"older inequality and power mean inequality, they obtain some integral inequalities related…

Classical Analysis and ODEs · Mathematics 2014-07-07 Mevlut Tunc , Sevil Balgecti

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are ({\alpha},m)-convex.

Classical Analysis and ODEs · Mathematics 2012-07-11 Imdat Iscan

In this work, we investigate the tensor inequalities in the tensor t-product formalism. The inequalities involving tensor power are proved to hold similarly as standard matrix scenarios. We then focus on the tensor norm inequalities. The…

Numerical Analysis · Mathematics 2021-08-10 Zhengbang Cao , Pengpeng Xie