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Inspired by the idea and technique in a recent paper of Huy et al. (Linear Algebra Appl 656: 368–384, 2023), Ighachane and Bouchangour showed an important refinement of the results by Sababheh (Linear Algebra Appl 506: 588–602, 2016) involving both convex and log-convex functions. In this paper, we continue to establish further new inequalities for both convex and log-convex functions with some applications to scalar and matrix means as well as matrix norm and numerical radius. The significance of the obtained results is two folded: the results themselves and the way they extend many known results in the literature. [ABSTRACT FROM AUTHOR]

In the present paper, we prove the monotonicity property of the ratios of the generalized Volterra function. As consequences, new and interesting monotonicity concerning ratios of the exponential integral function, as well as it yields some new functional inequalities including Turán-type inequalities. Moreover, two-side bounding inequalities are then obtained for the generalized Volterra function. The main mathematical tools are some integral inequalities. As applications, a few of upper and lower bound inequalities for the exponential integral function are derived. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples accompanied by graphical representations to substantiate the accuracy of the obtained results. Some potential directions for analogous further research on the subject of the present investigation are indicated in the concluding section. [ABSTRACT FROM AUTHOR]

This paper investigates a technique that uses Riemann-Liouville fractional integrals to study several Euler-Maclaurin-type inequalities for various function classes. Afterwards, we provide our results by using special cases of obtained theorems and This paper is to derive examples. Moreover, we give some Euler-Maclaurin-type inequalities for bounded functions by fractional integrals. Furthermore, we construct some fractional Euler-Maclaurin-type inequalities for Lipschitzian functions. Finally, we offer some Euler-Maclaurin-type inequalities by fractional integrals of bounded variation. [ABSTRACT FROM AUTHOR]

In this paper, we give some new sharp bounds for sinc and hyperbolic sinc functions via cosine and hyperbolic cosine functions, which these bounds refine or improve most of recent published results. [ABSTRACT FROM AUTHOR]

In the current research, some midpoint-type inequalities are generalized for co-ordinated convex functions with the help of generalized conformable fractional integrals. Moreover, some findings of this paper include results based on Riemann–Liouville fractional integrals and Riemann integrals. [ABSTRACT FROM AUTHOR]

In this paper, we first construct an integral identity associated with tempered fractional operators. By using this identity, we have found the error bounds for Simpson's second formula, namely Newton–Cotes quadrature formula for differentiable convex functions in the framework of tempered fractional integrals and classical calculus. Furthermore, it is also shown that the newly established inequalities are the extension of comparable inequalities inside the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove an equality for twice-differentiable convex functions involving the conformable fractional integrals. Moreover, several Bullen-type inequalities are established for twice-differentiable functions. More precisely, conformable fractional integrals are used to derive such inequalities. Furthermore, sundry significant inequalities are obtained by taking advantage of the convexity, Hölder inequality, and power-mean inequality. Finally, we provide our results by using special cases of obtained theorems. [ABSTRACT FROM AUTHOR]

In this paper we introduce necessary and sufficient conditions for a real-valued function to be preinvex. Some properties of preinvex functions and new versions of Jensen's integral type inequality in this setting are given. Several examples are also involved. [ABSTRACT FROM AUTHOR]

In this paper, an equality is proved for twice differentiable convex functions involving Riemann–Liouville fractional integral. With the help of this equality, there are established several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. By using special cases of the main results, previously obtained Simpson type inequalities are found for the Riemann–Liouville fractional integral. [ABSTRACT FROM AUTHOR]

In this paper, utilizing an identity given by Yıldız and Sarıkaya in (Yildiz and Sarikaya in Int. J. Anal. Appl. 13(1):64–69, 2017), we establish some weighted Ostrowski type inequalities for co-ordinated convex functions in a rectangle from the plane R 2 . Moreover, as special cases of our main results, we give some weighted Hermite–Hadamard type inequalities. The results given in this paper provide generalizations of some result established in earlier works. [ABSTRACT FROM AUTHOR]

In this paper, we present certain class of strictly positive definite functions related to the extended Hurwitz-Lerch Zeta function, digamma function and the modified Bessel function of first kind. The key tools in our proofs are some explicit formulas for the modified Bessel function of the first kind and a new integral representation of the extended Hurwitz-Lerch Zeta function when their terms contain the Fox H-function. As applications, monotonicity properties and some new functional inequalities of the aforementioned functions are established. [ABSTRACT FROM AUTHOR]

For a rational function r(z) having no zeros outside a unit disk, Li et al. (J Lond Math Soc 51:523–531, 1995) proved: | r ′ (z) | ≥ | B ′ (z) | | r (z) | , for | z | = 1 , where B (z) is the Blashke product. This result was improved and generalized in various ways and a recent generalization was obtained by Mir (Indian J Pure Appl Math 51:749–760, 2020). In this paper, we prove some results which include as special cases many Turán-type polynomial inequalities proved earlier. [ABSTRACT FROM AUTHOR]

In this paper, we establish an identity involving Sarikaya fractional integrals for twice differentiable functions. We obtain some new generalized fractional inequalities for the functions whose second derivatives in absolute value are convex by utilizing obtained equality. Utilizing the new inequalities obtained, some new inequalities for Riemann–Liouville fractional integrals and k-Riemann–Liouville fractional integrals are obtained. In addition, some of these results generalize ones obtained in earlier works. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an asymptotic expansion for the determinant of the matrix [ Ω n − i + j ] 1 ⩽ i , j ⩽ r , as n → ∞ , where Ω n denotes the volume of the unit ball in R n . [ABSTRACT FROM AUTHOR]

This paper deals with the arc lemniscate functions from the point view of bivariate means which have been introduced in [1]. In this study, several optimal bounds for these bivariate means in terms of arithmetic, geometric and quadratic means are established. As a consequence, new bounds for the arc lemniscate functions are also derived, which improve some previously known results. [ABSTRACT FROM AUTHOR]

In this paper, we determine the monotonicity of three classes of functions involving modified Bessel functions of the second kind. We also presented some inequalities and bounds for modified Bessel functions of the second kind. In particular, our results derive bounds for the Airy function and its derivative. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to established the modulus of derivative of rational functions r(z) having all its zeros in | z | ≤ k ≤ 1 , except two zeros z 0 and z 1 of multiplicity μ and ν respectively and some other related inequalities. The obtained results generalize and sharpen some well-known inequalities for the derivative of rational functions with prescribed poles and in turn produces some results besides the refinements of some polynomial inequalities as well. [ABSTRACT FROM AUTHOR]

In this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained. [ABSTRACT FROM AUTHOR]

In the paper, by virtue of convolution theorem for the Laplace transforms and analytic techniques, the author finds necessary and sufficient conditions for complete monotonicity, monotonicity, and inequalities of several functions involving polygamma functions. By these results, the author derives a lower bound of a function related to the sectional curvature of the Fisher–Rao manifold of beta distributions. [ABSTRACT FROM AUTHOR]

Simpson inequalities for differentiable convex functions and their fractional versions have been studied extensively. Simpson type inequalities for twice differentiable functions are also investigated. More precisely, Budak et al. established the first result on fractional Simpson inequality for twice differentiable functions. In the present article, we prove a new identity for twice differentiable functions. In addition to this, we establish several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. This paper is a new version of fractional Simpson type inequalities for twice differentiable functions. [ABSTRACT FROM AUTHOR]

In this paper, first we prove some new refinements of discrete weighted inequalities with negative powers on finite intervals. Next, by employing these inequalities, we prove that the self-improving property (backward propagation property) of the weighted discrete Muckenhoupt classes holds. The main results give exact values of the limit exponents as well as the new constants of the new classes. As an application, we establish the self-improving property (forward propagation property) of the discrete Gehring class. [ABSTRACT FROM AUTHOR]

In this paper, a new set of sufficient conditions are imposed on the parameters of the Fox H-functions, which allow us to conclude that it is non-negative. As applications, some classes of completely monotonic and positive definite functions involving the Fox H-function are established. Some new facts regarding the Fox-Wright functions, including complete monotonicity, logarithmic completely monotonicity and monotonicity of their ratios are discussed. [ABSTRACT FROM AUTHOR]

Several bounds of trigonometric-exponential and hyperbolic-exponential type for sinc and hyperbolic sinc functions are presented. In an attempt to generalize the results, some known inequalities are sharpened and extended. Hyperbolic versions are also established, along with extensions. [ABSTRACT FROM AUTHOR]

In this paper, we present several sharp bounds for the reciprocals of the Neuman-Sándor mean in terms of the harmonic, arithmetic, quadratic, and contraharmonic means by using classical analysis and inequalities theory. Finally, we give a remark based on the generalized trigonometric and generalized hyperbolic functions. [ABSTRACT FROM AUTHOR]

In mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which combines the proportional and Caputo operators. So we concentrate on the proportional Caputo-hybrid operator because of its numerous applications. In this research, we introduce a novel extension of the Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator and establish an identity. Then, taking into account this novel generalized identity, we develop some integral inequalities associated with the left-side of Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator. Moreover, to illustrate the newly established inequalities, we give some examples with the help of graphs. [ABSTRACT FROM AUTHOR]

In this current research, we focus on the domain of tempered fractional integrals, establishing a novel identity that serves as the cornerstone of our study. This identity paves the way for the Milne-type inequalities, which are explored through the framework of differentiable convex mappings inclusive of tempered fractional integrals. The significance of these mappings in the realm of fractional calculus is underscored by their ability to extend classical concepts into more complex, fractional dimensions. In addition, by using the Hölder inequality and power-mean inequality, we acquire some new Milne-type inequalities. Moreover, the practicality and theoretical relevance of our findings are further demonstrated through the application of specific cases derived from the theorems. [ABSTRACT FROM AUTHOR]

Fractional calculus is a crucial foundation in mathematics and applied sciences, serving as an extremely valuable tool. Besides, the new hybrid fractional operator, which combines proportional and Caputo operators, offers better applications in numerous fields of mathematics and computer sciences. Due to its wide range of applications, we focus on the proportional Caputo-hybrid operator in this research article. Firstly, we begin by establishing a novel identity for this operator. Then, based on the newfound identity, we establish some integral inequalities that are relevant to the left-hand side of Hermite–Hadamard-type inequalities for the proportional Caputo-hybrid operator. Furthermore, we show how the results improve upon and refine many previous findings in the setting of integral inequalities. Later, we present specific examples together with their related graphs to offer a better understanding of the newly obtained inequalities. Our results not only extend previous studies but also provide valuable viewpoints and methods for tackling a wide range of mathematical and scientific problems. [ABSTRACT FROM AUTHOR]