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In this paper, by the introduction of several parameters, we construct a new kernel function which is defined in the whole plane and includes some classical kernel functions. Estimating the weight functions with the techniques of real analysis, we establish a new Hilbert-type inequality in the whole plane, and the constant factor of the newly obtained inequality is proved to be the best possible. Additionally, by means of the partial fraction expansion of the tangent function, some special and interesting inequalities are presented at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduced the concept of multiplicatively p-convex functions and established Hermite-Hadamard type integral inequalities in the setting of multiplicative calculus for this newly created class of functions. We also gave integral inequalities of Hermite-Hadamard type for product and quotient of multiplicatively p-convex functions. Furthermore, we obtained novel multiplicative integral-based inequalities for the product and quotient of convex and multiplicatively p-convex functions. Additionally, we derived certain upper limits for this new class of functions. The findings we proved are generalizations of the results in the literature. The results obtained in this study may inspire further research in various scientific areas. [ABSTRACT FROM AUTHOR]

In this paper, the improvements in the estimations of some entropies are of our interest. These improvements can also be done sequentially. We find some new and refined bounds for the Tsallis entropy, Tsallis quasilinear entropy, and Tsallis quasilinear divergence. The estimations for the Tsallis entropy are provided with respect to the Shannon entropy and Rényi entropy. We obtain some alternative refined bounds for the Tsallis relative operator entropy and we establish the significant refined relation between the Tsallis relative operator entropy and the generalized relative operator entropy. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an equality involving tempered fractional integrals for twice-differentiable functions. By using this equality, we establish several left Hermite–Hadamard-type inequalities for the case of tempered fractional integrals. Moreover, we derive our results by using special cases of obtained theorems. [ABSTRACT FROM AUTHOR]

In this paper, with the help of Green's function and Hermite interpolating polynomial, an extension of Jensen's functional for n-convex functions is deduced from Jensen's inequality involving diamond integrals. Special Hermite conditions, including Taylor two point formula and Lagrange's interpolation, are also deployed to find the further extensions of Jensen's functional. This paper also includes discussion on bounds for Grüss inequality, Ostrowski inequality, and Čebyšev functional associated to the newly defined Jensen's functional. [ABSTRACT FROM AUTHOR]

In this paper, we first obtain an identity for differentiable mappings. Then, we establish some new generalized inequalities for differentiable convex functions involving some parameters and generalized fractional integrals. We show that these results reduce to several new Simpson-, midpoint- and trapezoid-type inequalities. The results given in this study are the generalizations of results proved in several earlier papers. [ABSTRACT FROM AUTHOR]

In this paper, we obtain inequalities for some integrals involving the modified Lommel function of the first kind t μ , ν (x) . In most cases, these inequalities are tight in certain limits. We also deduce a tight double inequality, involving the modified Lommel function t μ , ν (x) , for a generalized hypergeometric function. The inequalities obtained in this paper generalise recent bounds for integrals involving the modified Struve function of the first kind. [ABSTRACT FROM AUTHOR]

In this paper, we establish some Hardy inequalities for the p-Laplace operator associated with Robin boundary conditions in general domains. Moreover, by using the new Hardy inequality, we derive the classical Hardy inequality with the weight of mean distance function. [ABSTRACT FROM AUTHOR]

In this paper, we prove some new characterizations of two weighted functions u and v in norm inequalities of Hardy’s type, in the context of dynamic inequalities on time scales T . These norm inequalities studied the boundedness of the operator of Hardy’s type between the weighted spaces L v p (T) and L u q (T) . The paper covers the different cases when 1 < p ≤ q < ∞ and when 1 < q < p < ∞ . As special cases, when T = R , we obtain the corresponding previously known results from the literature, while for T = N we obtain some discrete results which are essentially new. In seeking applications, we will establish some non-oscillation results for second-order half-linear dynamic equations on time scales. [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]

Unfortunately, eleven of our provinces were severely affected due to two severe earthquakes that occurred in our country, the Republic of Turkey, on February 6, 2023. As a result, thousands of buildings were destroyed and tens of thousands of our citizens lost their lives. From past to present, such disasters have occurred in many parts of our world and will continue to happen. In order to raise awareness for researchers and academicians reading our article, we will give a new definition of convexity in this article, and we will call it "earthquake convexity". In this paper, we study some algebraic properties of the earthquake convexity. Then we compare the results obtained with both Hölder, Hölder–İşcan inequalities and power-mean, improved power-mean integral inequalities and show that the results obtained with Hölder–İşcan and improved power-mean inequalities are better than the others. Some applications to special means of real numbers are also given. [ABSTRACT FROM AUTHOR]

In this paper, a new integral identity is provided. Based on this equality, Simpson-type dual integral inequalities for functions whose first derivatives are s-convex via Riemann–Liouville fractional integrals are established. [ABSTRACT FROM AUTHOR]

The class of geometrically convex functions is a rich class that contains some important functions. In this paper, we further explore this class and present many interesting new properties, including fundamental inequalities, supermultiplicative type inequalities, Jensen-Mercer inequality, integral inequalities, and refined forms. The obtained results extend some celebrated results from the context of convexity to geometric convexity, with interesting applications to numerical inequalities for the hyperbolic and exponential functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce notable Jensen–Mercer inequality for a general class of convex functions, namely uniformly convex functions. We explore some interesting properties of such a class of functions along with some examples. As a result, we establish Hermite–Jensen–Mercer inequalities pertaining uniformly convex functions by considering the class of fractional integral operators. Moreover, we establish Mercer–Ostrowski inequalities for conformable integral operator via differentiable uniformly convex functions. Finally, we apply our inequalities to get estimations for normal probability distributions (Gaussian distributions). [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, we introduce a new Hermite-Hadamard type inequality by using post-quantum calculus for s-preinvex function and establish a new (p,q)-integral identity to derive some new Ostrowski type inequality for (p,q)-differentiable function. We give some application to special means for our newly proved inequalities. [ABSTRACT FROM AUTHOR]

Let Ω n = π n / 2 / Γ (n 2 + 1) (n ∈ N ) denote the volume of the unit ball in R n . In this paper, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions is presented, which yields a sharp double inequality for the quantity Ω n 2 / (Ω n − 1 Ω n + 1) . Also, we establish new sharp inequalities for the quantity Ω n 2 / (Ω n − 1 Ω n + 1) . [ABSTRACT FROM AUTHOR]

In this paper, we look at the general form of the two-point quadrature formulas, which doesn't have to be symmetric. Under the convexity constraint of the first derivative, we propose a new scheme that gives the best approximation of the two-point quadrature rules. [ABSTRACT FROM AUTHOR]

In this paper, based on a given parameterized identity that generates a quadrature rule family similar to Simpson's second formula, we establish some new Simpson-like type inequalities for functions with bounded as well as Lipchitzian derivatives from which we can deduce the famous 3/8-Simpson's inequality. The study concludes with an application example from management science. [ABSTRACT FROM AUTHOR]

In this paper, new inequalities for the left and right sides of the Hermite–Hadamard inequality are acquired for twice-differentiable mappings. Conformable fractional integrals are used to derive these inequalities. Furthermore, we provide our results by using special cases of obtained theorems. [ABSTRACT FROM AUTHOR]

The widely known hermite-hadamard-Fejer type inequalities are so important in the field of mathematical analysis. Many researchers have studied on these inequalities. In this paper, we have obtained several inequalities related to the Hermite-Hadamard inequality for a special class of the functions called uniformly convex functions. We have also presented applications of these obtained inequalities in some error estimates for higher moments of random variables. [ABSTRACT FROM AUTHOR]

In this paper the concept of symmetrized convex stochastic processes is introduced. Some characterizations involving Hermite–Hadamard type inequalities and a stability result for symmetrized convex stochastic processes are proved. [ABSTRACT FROM AUTHOR]

The Padé approximation is a useful method for creating new inequalities and improving certain inequalities. In this paper we use the Padé approximant to give the refinements of some remarkable inequalities involving inverse trigonometric functions, it is shown that the new inequalities presented in this paper are more refined than that obtained in earlier papers. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the self-improving property of the weighted Gehring class G λ p with a weight λ holds in the non-homogeneous spaces. The results give sharp bounds of exponents and will be used to obtain the self-improving property of the Muckenhoupt class A q . By using the rearrangement (nonincreasing rearrangement) of the functions and applying the Jensen inequality, we show that the results cover the cases of non-monotonic functions. For applications, we prove a higher integrability theorem and report that the solutions of partial differential equations can be solved in an extended space by using the self-improving property. Our approach in this paper is different from the ones used before and is based on proving some new inequalities of Hardy type designed for this purpose. [ABSTRACT FROM AUTHOR]

In this paper, we prove some new characterizations of weighted functions for dynamic inequalities of Hardy’s type involving monotonic functions on a time scale T in different spaces L p (T) and L q (T) when 0 < p < q < ∞ and p ≤ 1 . The main results will be proved by employing the reverse Hölder inequality, integration by parts, and the Fubini theorem on time scales. The main contribution in this paper is the new proof in the case when p < 1 , which has not been considered before on time scales. Moreover, the results unify and extend continuous and discrete systems under one theory. [ABSTRACT FROM AUTHOR]

This paper deals with generalizations and refinements of Fejér's inequality with some new applications. We introduce a real mapping M f ω (t) and obtain some its functional properties. We present several inequalities in connection with fractional integrals and their refinements by monotone functions. We also give some inequalities related to Euler's gamma and beta functions. Furthermore, we obtain some upper and lower bounds for generalized logarithmic mean and the expected value of random variables by using the arithmetic mean. [ABSTRACT FROM AUTHOR]

In this paper we deal with functions related to generalized convexity and refine Jensen type inequalities satisfied by such functions. Specifically, we extend inequalities satisfied by uniformly convex functions, strongly convex functions as well as superquadratic functions. [ABSTRACT FROM AUTHOR]

In this paper, we first prove a new parameterized identity that generates a quadrature rule family similar to Simpson's second formula, and then we establish some new Simpson-like type inequalities for functions whose first derivatives are s-convex in the second sense, from which we can deduce the famous 3 8 -Simpson inequality. We end the article with some applications. [ABSTRACT FROM AUTHOR]

In the paper, the authors present the Schur m-power convexity and concavity for the general geometric Bonferroni mean of multiple parameters and establish comparison inequalities for bounding the general geometric Bonferroni mean in terms of the arithmetic, geometric, and harmonic means. These Schur convexity and concavity provide a unified generalization of the Schur convexity and concavity for the geometric Bonferroni means of two or three parameters. [ABSTRACT FROM AUTHOR]

In this paper, we study the norm and skew angular distances in a normed space X , where convex functions are used to obtain refinements and reverses of some outstanding results in the literature. For example, in this regard, we show that if a , b ∈ X are non-zero and if p , q > 0 are such that 1 p + 1 q = 1 , then 2 λ p r a r + q r b r 2 - p a + q b 2 r ≤ p r - 1 a r + q r - 1 b r - a + b r ≤ 2 μ p r a r + q r b r 2 - p a + q b 2 r , where r ≥ 1 , λ = min 1 / p , 1 / q and μ = max 1 / p , 1 / q . Then we explain how this result extends some known results in the literature. Many other related results will be also shown. Then, with the theme of convexity, we employ a log-convex approach on certain matrix functions to obtain improvements and new sights of some matrix inequalities, including possible bounds of ‖ A t X B 1 - t ‖ , where A, B are positive definite matrices, X is an arbitrary matrix, ‖ · ‖ is a unitarily invariant norm and 0 ≤ t ≤ 1. Many other results involving matrix and scalar log-convex functions will be presented too. [ABSTRACT FROM AUTHOR]

In this article, we introduce a class of functions U (p) with integral representation defined over a measure space with σ-finite measure. The main purpose of this paper is to extend the Minkowski and related inequalities by considering general kernels. As a consequence of our general results, we connect our results with various variants for the fractional integrals operators. Such applications have wide use and importance in the field of applied sciences. [ABSTRACT FROM AUTHOR]

Inequalities play a major role in pure and applied mathematics. In particular, the inequality plays an important role in the study of Rosseland's integral for the stellar absorption. In this paper we obtain new Milne-type inequalities, and we apply them to the generalized Riemann–Liouville-type integral operators, which include most of the known Riemann–Liouville integral operators. [ABSTRACT FROM AUTHOR]

In this paper we introduce the concept of pre-Schur convex functions defined on general domains from plane. Then, by making use of Green's identity for double integrals, we establish some integral inequalities for this class of functions that naturally generalize the case of Schur convex functions. Some exmples for rectangles and disks are also provided. [ABSTRACT FROM AUTHOR]

We study lower estimates for integral fuctionals for which the structure of the integrand is defined by a graph, in particular, by a bipartite graph. Functionals of such kind appear in statistical mechanics and quantum chemistry in the context of Mayer's transformation and Mayer's cluster integrals. Integral functionals generated by graphs play an important role in the theory of graph limits. Specific kind of functionals generated by bipartite graphs are at the center of the famous and much studied Sidorenko's conjecture, where a certain lower bound is conjectured to hold for every bipartite graph. In the present paper we work with functionals more general and lower bounds significantly sharper than those in Sidorenko's conjecture. In his 1991 seminal paper, Sidorenko proved such sharper bounds for several classes of bipartite graphs. To obtain his result he used a certain way of "gluing" graphs. We prove his inequality for a new class of bipartite graphs by defining a different type of gluing. [ABSTRACT FROM AUTHOR]