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In this paper, we consider homogeneous quasideviation means generated by real functions (defined on (0, ∞)) which are concave around the point 1 and possess certain upper estimates near 0 and ∞. It turns out that their concave envelopes can be completely determined. Using this description, we establish su˚cient conditions for the Hardy property of the homogeneous quasideviation mean and we also furnish an upper estimates for its Hardy constant. [ABSTRACT FROM AUTHOR]

In this paper, we solve the question completely raised by Feng Qi and Dongkyu Lim in paper "Monotonicity properties for a ratio of finite many gamma functions" published in Advances in Difference Equations and get some properties about ratios of finitely many gamma functions such as complete monotonicity, logarithmically complete monotonicity, the Bernstein function property, null point and extreme value. [ABSTRACT FROM AUTHOR]

This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite–Hadamard type are derived for this class of functions using the Hölder–İşcan integral inequality. The results obtained in this paper are compared with those known in the literature, demonstrating the superiority of the new results. Finally, some applications for special means are provided. [ABSTRACT FROM AUTHOR]

In the paper, we study dynamic h-convexity for interval valued functions. Some generalizations of Jensen's inequality in interval valued analysis for h-convex functions on time scales are proved in the paper. In seek of applications of generalized Jensen's inequality, Hermite-Hadamard type inequalities for h-convex functions on time scales are established. Further discrete analogues of newly proved results are also presented in the paper. Some numerical examples are also provided to check the validity of the results. [ABSTRACT FROM AUTHOR]

This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences. [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 establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder's inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when T = N and T = R ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011). [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 introduce a biparametrized multiplicative integral identity and employ it to establish a collection of inequalities for multiplicatively convex mappings. These inequalities encompass several novel findings and refinements of established results. To enhance readers' comprehension, we offer illustrative examples that highlight appropriate choices of multiplicatively convex mappings along with graphical representations. Finally, we demonstrate the applicability of our results to special means of real numbers within the realm of multiplicative calculus. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of strongly generalized convex functions which is called as strongly η-convex stochastic processes. We prove the Hermite-Hadamard, Ostrowski type inequality, and obtain some important inequalities for above processes. Some previous results are special cases of the results obtained in this paper. [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 first introduce four new generalized quantum integrals of two variables functions which are called T q -integrals. We also give some examples of each of these given integrals. Then we establish corresponding T q -Hermite–Hadamard type inequalities for co-ordinated convex functions. In order to show correctness of our results, we apply our main theorems to several co-ordinated convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we prove Rubio de Francia extrapolation results for pair of non-increasing functions with B p (·) weights. The case of B ∞ weights has also been proved. These results have been applied to obtain the extrapolation results in the framework of variable exponent Lebesgue space L w p (·) with Luxemburg norm. Also, an improved norm estimate for the boundedness of Hardy averaging operator on variable exponent Lebesgue space is given. [ABSTRACT FROM AUTHOR]

The authors of the paper suggest a novel approach in order to examine an integral equality using conformable fractional operators. By using this identity, some Newton-type inequalities are proved for differentiable convex functions by taking the modulus of the newly established equality. Moreover, we prove some Newton-type inequalities by using the Hölder and power-mean inequality. Furthermore, some new results are presented by using special choices of obtained inequalities. Finally, we give some conformable fractional Newton-type inequalities for functions of bounded variation. [ABSTRACT FROM AUTHOR]

As a first attempt, we obtain the boundedness of the rough fractional Hausdorff operator on variable exponent Herz-type spaces. The method used in this paper enables us to study the operator on some other function spaces with variable exponents. [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, by considering the identity established by Luo et al. in [C. Luo, T.-S. Du, M. Kunt and Y. Zhang, Certain new bounds considering the weighted Simpson-like type inequality and applications, J. Inequal. Appl. 2018 2018, Paper No. 332] and under the assumption of the quasi-convexity of the first derivative, we establish some new error estimates of the Simpson-like type inequalities. We also discuss the case where the first derivative satisfies the Hölder condition. At the end, we provide some applications to special means. The obtained results represent a continuation of the above-mentioned paper. [ABSTRACT FROM AUTHOR]

Recently, we have obtained two general theorems dealing with | N ¯ , p n | k summability factors of infinite series and trigonometric Fourier series (Bor in Bull Sci Math 169:102990, 2021) by using almost increasing sequences. In this paper, we have generalized these theorems to | N ¯ , p n ; θ n | k summability methods. Some new and known results are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we prove some operator inequalities associated with an extension of the Kantorovich type inequality for s-convex functions. We also give an application to the order preserving power inequality of three variables and find a better lower bound for the numerical radius of a positive operator under some conditions. [ABSTRACT FROM AUTHOR]

In this paper, we develop a concept of a logarithmically superquadratic function. Such a class of functions is defined via superquadratic functions. We first establish some new properties of superquadratic functions. In particular, we derive the corresponding superadditivity relation and its reverse, as well as the external form of the Jensen inequality and its reverse. Then, as a direct consequence of the established results, we obtain the corresponding properties for logarithmically superquadratic functions. Further, we show that logarithmically superquadratic functions with values greater than or equal to one are convex and logarithmically superadditive. In particular, we also obtain the corresponding refinement of the Jensen inequality in a product form. Finally, we give a variant of the Jensen operator inequality for logarithmically superquadratic functions. [ABSTRACT FROM AUTHOR]

In this paper, we obtain several Adams-type inequalities with logarithmic weights on the unit ball B in R n , where n ≥ 3 . Firstly, we show that for any β ∈ 0 , 1 , the following critical Adams' inequality sup u ∈ W 0 , r 2 , n 2 (B , ω) , u ω ≤ 1 ∫ B exp α u n n - 2 1 - β d x < ∞ holds if and only if α ≤ α β = n n - 2 n 2 n V n 2 n - 2 1 - β 1 - β 1 1 - β , where V n = π n 2 Γ n 2 + 1 is the volume of the unit ball B in R n , W 0 , r 2 , n 2 (B , ω) is the radial weighted Sobolev space under the norm u ω = ∫ B Δ u n 2 ω x d x 2 n with ω (x) = log 1 x β (n 2 - 1) or ω (x) = log e x β (n 2 - 1) . Secondly, we prove the following two supercritical Adams' inequalities sup u ∈ W 0 , r 2 , n 2 (B , ω) , u ω ≤ 1 ∫ B exp α β + x m u n n - 2 1 - β d x < ∞ and sup u ∈ W 0 , r 2 , n 2 (B , ω) , u ω ≤ 1 ∫ B exp α β u n n - 2 1 - β + x m d x < ∞ , where m is some positive number. Moreover, we prove the existence of extremals for these Adams-type inequalities. [ABSTRACT FROM AUTHOR]

Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field. [ABSTRACT FROM AUTHOR]

In this paper, we discuss new iterated discrete inequalities of Hardy type involving matrix kernels. Under some conditions on matrix entries of the kernels, we establish weight characterizations of these inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we establish several new inequalities for q-differentiable coordinated convex functions that are related to the right side of Hermite–Hadamard inequalities for coordinated convex functions. We also show that the inequalities proved in this paper generalize the results given in earlier works. Moreover, we give some examples in order to demonstrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new (p , q) -integral inequalities of Simpson's second type for preinvex functions. Many results given in this paper provide generalizations and extensions of the results given in previous research. Moreover, some examples are given to illustrate the investigated results. [ABSTRACT FROM AUTHOR]

In this paper we give some new power-type refinements and reverses of the weighted arithmetic–geometric mean inequality. Our result is a remarkable generalization of the one due to Furuichi (J Math Inequal 5(1):21–31, 2011), Manasrah and Kittaneh (J Math Anal Appl 361(1):262–269, 2010, Linear Multilinear Algebra 59(9):1031–1037, 2011). When the power is a positive integer number, our result is also a refinement of a very recent generalization established by Ighachane et al. (Math Inequal Appl 23(3):1079–1085, 2020) for this inequality. As an application, we provide some generalized inequalities for determinants of positive definite matrices. [ABSTRACT FROM AUTHOR]

This paper adopts different optimization algorithms such as Genetic Algorithm (GA) and Particle Swarm Optimization Algorithm (PSO-Algorithm) to train Back-Propagation (BP) neural networks, fits the Chinese, the Czech, Slovak, Hungarian, and Polish gross domestic product (GDP) growth model (from 1995 to 2020) and makes short-term simulation predictions. We use the PSO-Algorithm and GA with strong global search ability to optimize the weights and thresholds of the network, combine them with the BP neural network, and apply the resulting Particle Swarm Optimization Back-Propagation (PSO-BP) combined model or Genetic-Algorithm Back-Propagation (GA-BP) combined model to allow the network to achieve fast convergence. Besides, we also compare the above two hybrid models with standard multivariate regression model and BP neural network with different initialization methods like normal uniform and Xavier for fitting and short-term simulation predictions. Finally, we obtain the excellent results that all the above models have achieved a good fitting effect and PSO-BP combined model on the whole has a smaller error than others in predicting GDP values. Through the technology of PSO-BP and GA-BP, we have a clearer understanding of the five countries gross domestic product growth trends, which is conducive to the government to make reasonable decisions on the economic development. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Minkowski integral inequality on time scales by Δ Δ -integral and the inverse Minkowski inequality over the set of constant sign functions. We get similar results by replacing Δ Δ -integral with Δ ∇ , ∇ Δ and ∇ ∇ -integrals. For application, we give another proof of the Hardy inequality on time scales according to the Minkowski inequality. [ABSTRACT FROM AUTHOR]

This paper aims to extend the application of the Ostrowski inequality, a crucial tool for figuring out the error bounds of various numerical quadrature rules, including Simpson's, trapezoidal, and midpoint rules. Specifically, we develop a more comprehensive class of Ostrowski-type inequalities by utilizing the weighted version of Riemann–Liouville (RL) fractional integrals on an increasing function. We apply our findings to estimate the error bounds of Hadamard-type inequalities. Our results are more comprehensive, since we obtain the results of the existing literatures as particular cases for certain parameter values. This research motivates researchers to apply this concept to other fractional operators. [ABSTRACT FROM AUTHOR]

This paper proves an equality for the case of differentiable convex functions including the conformable fractional integrals. By using this equality, we establish several parameterized inequalities with the help of the conformable fractional integrals. Several inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Furthermore, we present previously achieved results and new results by using special cases of the obtained theorems. [ABSTRACT FROM AUTHOR]

Based on the uncertainty theory, Liu [B. Liu, Some research problems in uncertainty theory, J. Uncertain Syst. 3 2009, 1, 3–10] introduced an uncertain integral for applying uncertain differential equation, finance, control, filtering and dynamical systems. Since uncertain integrals are the important content of uncertainty theory, this paper explores an approach of the relationship between uncertain integrals by the well-known Chebyshev-type inequality. Also, we propose the concept of an uncertain fractional integral which is generalized version of an uncertain integral. The definition of a strong comonotonic uncertain process and some new properties of the uncertain integral were presented in [C. You and N. Xiang, Some properties of uncertain integral, Iran. J. Fuzzy Syst. 15 2018, 2, 133–142]. Based on the strong comonotonic uncertain process, as an application, we provide Chebyshev's inequality for a fractional uncertain integral and an uncertain integral. [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]