Article
Mathematics, Applied
Wen-Hui Li, Peng Miao, Bai-Ni Guo
Summary: In this paper, the authors provide sharp upper and lower bounds for the Neuman-Sandor mean and present new inequalities involving hyperbolic sine and cosine functions.
Article
Mathematics, Applied
Muhammad Amer Latif
Summary: In this study, mappings related to Fejer-type inequalities for harmonically convex functions are defined over [0, 1]. These mappings are used to prove Fejer-type inequalities for harmonically convex functions and obtain refinements of some known results.
Article
Mathematics
Mengyan Xie, Jiao Zhang
Summary: This paper provides upper and lower bounds for the weighted arithmetic mean, geometric mean, and harmonic mean of a set of sector matrices, extending previous results by Sagae and Tanabe. In application, the study presents inequalities for singular values, determinants, and unitarily invariant norms.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Mathematics
Horst Alzer, Ahmed Salem
Summary: The study by Kairies in 1984 showed that for positive real numbers x, the geometric mean of Gamma(q)(x) and Gamma(q)(1/x) is greater than or equal to 1 if q is not equal to 1. This result can be further improved if q is an element of (0,1).
Article
Multidisciplinary Sciences
Muhammad Amer Latif
Summary: This paper introduces mappings related to Fejer-type inequalities for harmonically convex functions defined on [0,1], and obtains companions of Fejer-type inequalities for harmonically convex functions using these mappings. The properties of these mappings are discussed, leading to refinement inequalities of some known results.
Article
Mathematics, Applied
Abdul Wakil Baidar, Mehmet Kunt
Summary: In this manuscript, we introduce the concept of GA-s-convex functions in the fourth sense and derive the Hermite-Hadamard inequality for this newly introduced class of functions. We also establish some Hermite-Hadamard type inequalities for functions whose absolute value of the first derivative at certain powers is a GA-s-convex function in the fourth sense. Finally, we provide some applications to special means of real numbers.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Chao-Ping Chen
Summary: In this paper, certain asymptotic expansions and inequalities for the Apery constant are presented. The results are based on the series representations of the Apery constant. For example, based on Gosper's result zeta(3) = 1/4 Sigma(infinity)(k=1) 30k-11/(2k - 1)k(3) ((2k)(k))(2), the following asymptotic expansion of the remainder R-n is established: R-n = 1/4 Sigma(infinity)(k=n+1) 30k-11/(2k - 1)k(3) ((2k)(k))(2) similar to pi/n(2)2(4n+2) {1 - 7/4n + 81/32n(2) - 489/128n(3) + 13787/2048 - ... }, as n -> infinity. Moreover, a formula for determining the coefficients in the expansion is given. Inequalities for the Apery constant are also proven.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2022)
Article
Mathematics, Interdisciplinary Applications
Arslan Razzaq, Tahir Rasheed, Shahid Shaokat
Summary: In this paper, a new generalized F-convexity and related integral inequalities on fractal sets are presented. These developments result in new bounds for integral inequalities. New generalized Hermite-Hadamard type inequalities in the fractal sense are also introduced. The paper proposes new results by employing local fractional calculus and new definitions for twice differentiable functions. Additionally, new inequalities for midpoint and trapezoid formula for a new class of local fractional calculus are given.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics
Josip Pecaric, Jurica Peric, Sanja Varosanec
Summary: We provide a refinement of the converse Holder inequality for functionals by using an interpolation result for Jensen's inequality. In addition, we improve the converse of the Beckenbach inequality. We also consider the converse Minkowski inequality for functionals and give refinements of it, along with applications on integral mixed means.
Article
Mathematics
Ling Zhu
Summary: The upper and lower bounds in the form of simple rational functions about cosht and (sinht)/t for the function I0x are obtained, and the corresponding inequalities for the Toader-Qi mean do not match those in the existing literature.
Article
Mathematics
Hari M. Srivastava, Sana Mehrez, Sergei M. Sitnik
Summary: In this paper, new generalizations of Hermite-Hadamard-type inequalities are established. These inequalities are formulated in terms of modules of certain powers of proper functions. Generalizations for convex functions are also considered. As applications, new inequalities for the digamma function in terms of the trigamma function and some inequalities involving special means of real numbers are given. The results also include estimates via arithmetic, geometric and logarithmic means. The examples demonstrate the improved accuracy of some of the results in this paper compared to the existing ones.
Article
Mathematics, Applied
Muhammad Amer Latif
Summary: In this study, new functionals linked with weighted integral inequalities for harmonic convex functions are introduced. Additionally, new inequalities of the Fejer type are discovered.
Article
Mathematics, Interdisciplinary Applications
Hijaz Ahmad, Muhammad Tariq, Soubhagya Kumar Sahoo, Jamel Baili, Clemente Cesarano
Summary: This paper introduces some generalized integral inequalities of the Raina type depicting the Mittag-Leffler function and explores the idea of generalized s-type convex function of Raina type. It discusses algebraic properties and establishes a novel version of the Hermite-Hadamard inequality, along with some refinements and valuable applications. The results presented in this paper can be seen as a significant improvement of previously known results.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics
Muhammad Tariq, Soubhagya Kumar Sahoo, Sotiris K. Ntouyas, Omar Mutab Alsalami, Asif Ali Shaikh, Kamsing Nonlaopon
Summary: This article discusses the importance of convex analysis and integral inequalities in mathematical interpretation and their applications in various sciences. It introduces a new concept of generalized harmonic convexity and establishes new integral identities as well as refinements of existing inequalities. The results contribute to the generalization of prior research.
Article
Multidisciplinary Sciences
Anna Dobosz, Piotr Jastrzebski, Adam Lecko
Summary: This paper studies a certain differential subordination related to the harmonic mean and its symmetry properties, with a focus on the case where the dominant is a linear function. In addition to known results, the paper explores differential subordinations for selected convex functions and the search for the best dominant function or one close to it. The differential subordination of the harmonic mean is a generalization of the Briot-Bouquet differential subordination in this context.
