Type Inequalities Research Articles

A new version of Boole's formula type inequalities in multiplicative calculus with application to quadrature formula

A new version of Boole's formula type inequalities in multiplicative calculus with application to quadrature formula

Symmetric midpoint type inequalities for (α, m)-Convex Functions with Applications

Symmetric midpoint type inequalities for (α, <i>m</i>)-Convex Functions with Applications

Two twinning operators when imposing nonlinear modulation in short‐time Fourier transform

Two types of short‐time Fourier transforms involving respectively nonlinear modulation and nonlinear translation are designed in this note. Some important properties such as twin in time‐frequency domain and orthogonality relations are investigated. Moreover, Lieb type inequalities and uncertainty principle are established.

Generalization of some integral inequalities in multiplicative calculus with their computational analysis

UDC 517.9 We focus on generalizing some multiplicative integral inequalities for twice differentiable functions. First, we derive a multiplicative integral identity for multiplicatively twice differentiable functions. Then, with the help of the integral identity, we prove a family of integral inequalities, such as Simpson, Hermite–Hadamard, midpoint, trapezoid, and Bullen types inequalities for multiplicatively convex functions. Moreover, we provide some numerical examples and computational analysis of these newly established inequalities to prove the validity of the results for multiplicatively convex functions. The generalized forms obtained in our research offer valuable tools for researchers in various fields.

Some New Fractional Hermite-Hadamard type Inequalities For Generalized Class of Godunova-Levin Functions By Means of Interval Center-Radius OrderRelation with Applications

Some New Fractional Hermite-Hadamard type Inequalities For Generalized Class of Godunova-Levin Functions By Means of Interval Center-Radius OrderRelation with Applications

Some Geraghty Type Inequalities in b-fuzzy Metric Spaces with an Application

In this note, we introduce novel Geraghty-type inequalities within the framework of a b-fuzzy metric space and develop new fixed point theorems for such mappings in a G-complete b-fuzzy metric space. To substantiate our findings, we present several illustrative examples using graphical methods. Additionally, we demonstrate the application of our introduced theorems by solving a non-linear integral equation, showing the practical utility of our results.

On strongly m-convex stochastic processes

AbstractIn this paper, we introduce the concept of strongly m-convex stochastic processes and present some basic properties of these stochastic processes. We derive Hermite-Hadamard type inequalities for stochastic processes whose first derivatives in absolute values are strongly m-convex. The results presented in this paper are a generalization and extension of previously known results.

Arbitrary Random Variables and Wiman’s Inequality

We study the class of random entire functions given by power series, in which the coefficients are formed as the product of an arbitrary sequence of complex numbers and two sequences of random variables. One of them is the Rademacher sequence, and the other is an arbitrary complex-valued sequence from the class of sequences of random variables, determined by a certain restriction on the growth of absolute moments of a fixed degree from the maximum of the module of each finite subset of random variables. In the paper we prove sharp Wiman–Valiron’s type inequality for such random entire functions, which for given p∈(0;1) holds with a probability p outside some set of finite logarithmic measure. We also considered another class of random entire functions given by power series with coefficients, which, as above, are pairwise products of the elements of an arbitrary sequence of complex numbers and a sequence of complex-valued random variables described above. In this case, similar new statements about not improvable inequalities are also obtained.

On q-Hermite–Hadamard–Mercer and midpoint-Mercer inequalities for general convex functions with their computational analysis

This paper establishes some new inequalities of Hermite–Hadamard–Mercer type for [Formula: see text]-convex functions in the framework of [Formula: see text]-calculus and classical calculus. Some new [Formula: see text]-midpoint-Mercer type inequalities for the [Formula: see text]-differentiable [Formula: see text]-convex functions are also proved. Moreover, the computational analysis of newly established inequalities for convex and [Formula: see text]-convex functions are given to prove that the bounds of this paper are better than those of the existing ones. It is also shown with mathematical examples that the newly established inequalities are valid for [Formula: see text]-convex functions in [Formula: see text]-calculus.

Do poor psychosocial resources mediate health inequalities in type 2 diabetes? The Maastricht Study

Abstract Low socioeconomic position (SEP) has been identified as a risk factor for type 2 diabetes mellitus (T2DM). A potential pathway of this association is psychosocial resources. Disadvantageous environmental conditions result in low control beliefs through adverse resources and inferiority beliefs through social comparison for people with a low SEP. We examined two poor psychosocial resources, low control beliefs and inferiority beliefs, to explain socioeconomic inequalities in T2DM. We analysed mediating roles of low control beliefs and inferiority beliefs by using counterfactual mediation analysis. 8293 participants aged 40-75 living in Limburg, the Netherlands participated in The Maastricht Study starting from September 2010 to October 2020 and were followed up to 10 years with annual questionnaires with a median follow-up time of 7.18 years. SEP (education, income, occupation), control and inferiority beliefs, and (pre)diabetes by oral glucose tolerance test were measured at baseline. Incident T2DM was self-reported per annum. 3.2%(N = 203) of the participants without T2DM at baseline reported incident T2DM. People with low SEP had more often prevalent and incident T2DM (e.g., low education:HR=2.13, 95%CI:1.53-2.97). Lower control beliefs and higher inferiority beliefs were more common among people with low SEP than people with high SEP. Moreover, lower control beliefs and higher inferiority beliefs were risk factors for T2DM (e.g., low control beliefs: HR = 1.50, 95%CI:1.08-2.09). The relationship between SEP and T2DM was partially mediated by control beliefs (7.98-13.56%) and inferiority beliefs (2.16-4.53%). Poor psychosocial resources are important in socioeconomic inequalities in diabetes. Researchers and practitioners should consider the psychosocial profile of people with lower SEP might differ from those with higher SEP and this might interfere with the development, treatment, and prevention of T2DM. We should aim to work with such beliefs, instead of against it. Key messages • Socioeconomic health inequalities in diabetes has many underlying mechanism including psychosocial pathways. • Interventions and research should consider the different environment of low SEP and psychosocial profiles of people. We should aim to work with it, instead of against it.

Equity of continuous glucose monitoring in young people with type 1 diabetes: a systematic review

Abstract Background Socioeconomic (SES) and ethnic inequalities in type 1 diabetes (T1D) outcomes are widespread. There is concern that unequal access to technologies, such as continuous glucose monitoring (CGM), may increase disparities. This systematic review summarises the evidence for inequalities in access to CGM for children and young people (CYP) and outcomes for CGM users. Methods MEDLINE, Embase, and Web of Science were searched for observational studies published between January 2020 and July 2023 which report CGM use stratified by any PROGRESS-plus criteria for T1D patients under 26. Reports based in low- or middle-income countries or ≤ 500 participants were excluded. Primary outcomes were the proportion of patients using CGM and HbA1c of CGM users. Quality assessment was performed using the Newcastle-Ottawa Scale. Unadjusted odds ratios were calculated from extracted data, though heterogeneity precluded meta-analysis. The protocol was pre-registered with PROSPERO (CRD42023438139). Results Of the 3,369 unique studies identified, 27 met inclusion criteria. We found decreased CGM use and higher discontinuation for low SES, low education, publicly insured, and minority ethnic, especially black, CYP. These associations were generally robust to adjustment for other sociodemographic variables, suggesting an independent effect. Lower SES inequalities were seen in countries where CGM is reimbursed. Although low SES and minority ethnicity were generally associated with poorer outcomes, there was no significant association between domains of disadvantage and higher HbA1c for CGM users, excepting parental education. Conclusions There are significant SES, ethnic, and education inequalities in CGM use for CYP with T1D, particularly when reimbursement is limited. This is contributing to outcome inequalities. However, evidence suggests CYP benefit equally from CGM use, irrespective of ethnicity and SES. Increasing CGM funding and use is likely to reduce outcome inequalities. Key messages • There are significant SES, ethnic, and education inequalities in continuous glucose monitoring use for young people with T1D. Inequalities are more marked when technology is not reimbursed. • Increasing access to CGM may reduce outcome inequalities, as evidence suggests that young people benefit equally from CGM use, regardless of ethnicity or SES.

Concentration of ground state solutions for supercritical zero-mass (N, q)-equations of Choquard reaction

We study the following singularly perturbed (N, q)-equation of Choquard type -εNΔNu-εqΔqu=εμ-N(∫RNK(y)F(u(y))|x-y|μdy)K(x)f(u),x∈RN,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} -\\varepsilon ^N\\Delta _Nu-\\varepsilon ^q\\Delta _qu=\\varepsilon ^{\\mu -N} \\bigg (\\int _{\\mathbb {R}^N}\\frac{K(y)F(u(y))}{|x-y|^{\\mu }}dy\\bigg )K(x)f(u),~x\\in \\mathbb {R}^N, \\end{aligned}$$\\end{document}where Δru=div(|∇u|r-2∇u)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta _ru = \ ext {div}(|\ abla u|^{r-2}\ abla u)$$\\end{document} denotes the usual r-Laplacian operator with r∈{q,N}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r\\in \\{q,N\\}$$\\end{document} and 1<q<N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1<q<N$$\\end{document}, ε>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon >0$$\\end{document} is a sufficiently small parameter, K∈C0(RN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K\\in C^0(\\mathbb {R}^N)$$\\end{document} satisfies some technical assumptions, 0<μ<N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0<\\mu <N$$\\end{document} and F is the primitive of f that fulfills a supercritical exponential growth in the Trudinger–Moser sense. Due to the new version of Trudinger–Moser type inequality introduced in Shen and Rădulescu (Zero-mass (N, q)-Laplacian equation with Stein-Weiss convolution part in RN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^N$$\\end{document}: supercritical exponential case. submitted), we aim to derive the existence and concentration of ground state solutions for the given equation using variational method, where the concentrating phenomenon appears at the maximum point set of K as ε→0+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon \\rightarrow 0^+$$\\end{document}.

Violation of LGtI inequalities in the light of NOν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document}A and T2K anomaly

The recent anomaly observed in NOν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document}A and T2K experiments in standard three-flavor neutrino oscillation could potentially signal physics extending beyond the standard model (SM). For the NSI parameters that can accommodate this anomaly, we explore the violation of Leggett–Garg type inequalities (LGtI) within the context of three-flavor neutrino oscillations. Our analysis focuses on LGtI violations in scenarios involving complex NSI with ϵeμ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon _{e\\mu }$$\\end{document} or ϵeτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon _{e\ au }$$\\end{document} coupling in long baseline accelerator experiments for normal and inverted mass ordering. LGtI violation is significantly enhanced in normal ordering (NO) for ϵeτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon _{e\ au }$$\\end{document} scenario for T2K, NOν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document}A, and DUNE experiment set-up. We find that for inverted ordering (IO), in the DUNE experimental set-up above 8.5 GeV, the LGtI violation can be an indication of ϵeτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon _{e\ au }$$\\end{document} new physics scenario.

ANALYSIS ON MULTIPLICATIVELY (P,m)-SUPERQUADRATIC FUNCTIONS AND RELATED FRACTIONAL INEQUALITIES WITH APPLICATIONS

In this work, we, for the first time, establish a class of multiplicatively [Formula: see text]-superquadratic function and look into its various features. In the light of these features, we come up with the several integer order integral inequalities in the frame of multiplicative calculus. Moreover, we develop the fractional version of Hermite–Hadamard’s type inequalities involving midpoints and end points for multiplicatively [Formula: see text]-superquadratic function with respect to multiplicatively [Formula: see text]-Riemann–Liouville fractional integrals. By choosing different values for the parameters of such integral operators, we acquire a simple version of integral inequalities of Hermite–Hadamard’s type as well as its fractional form via multiplicatively Riemann–Liouville fractional integrals for multiplicatively [Formula: see text]-superquadratic function. The findings are confirmed by graphical illustration by taking appropriate examples into account. The study is further enhanced by the addition of applications of special means and first-type modified Bessel functions. The new results clearly provide extensions and improvements of the work available in the literature.

Stability of Alexandrov–Fenchel Type Inequalities for Nearly Spherical Sets in Space Forms

Stability of Alexandrov–Fenchel Type Inequalities for Nearly Spherical Sets in Space Forms

Generalized Tensorial Simpson type Inequalities for Convex functions of Selfadjoint Operators in Hilbert Space

Several generalized Simpson tensorial type inequalities for self adjoint operators have been obtained with variation depending on the conditions imposed on the function f.

Some inequality and Berezin number type inequalities

Some inequality and Berezin number type inequalities

FACTORIZATIONS AND UNIFIED HARDY INEQUALITIES ON HOMOGENEOUS LIE GROUPS

In this note we obtain Hardy and critical Hardy inequalities with any homogeneous quasi-norm in unified way. Actually, we show a sharp remainder formula for these results. In particular, our identity implies corresponding Hardy and critical Hardy inequalities with any homogeneous quasi-norm for the radial derivative operator, thus yielding improved versions of corresponding classical counterparts. Moreover, we discuss extensions of these results in the setting of Folland and Stein’s homogeneous Lie groups. Such a more general setting is convenient for the distillation of those results of harmonic analysis depending only on the group and dilation structures, which is one of our motivations working in the setting. Our approach based on the factorization method of differential operators introduced by Gesztesy and Littlejohn. As an application, we show Caffarelli-Kohn-Nirenberg type inequalities with more general weight. Because of the freedom in the choice of any homogeneous quasi-norm, our results give new insights already in both anisotropic ℝn and isotropic ℝn .

Revised logarithmic Sobolev inequalities of fractional order

In this short note we prove the logarithmic Sobolev inequality with derivatives of fractional order on Rn with an explicit expression for the constant. Namely, we show that for all 0<s<n2 and a>0 we have the inequality∫Rn|f(x)|2log⁡(|f(x)|2‖f‖L2(Rn)2)dx+ns(1+log⁡a)‖f‖L2(Rn)2≤C(n,s,a)‖(−Δ)s/2f‖L2(Rn)2 with an explicit C(n,s,a) depending on a, the order s, and the dimension n, and investigate the behaviour of C(n,s,a) for large n. Notably, for large n and when s=1, the constant C(n,1,a) is asymptotically the same as the sharp constant of Lieb and Loss that was computed in [13]. Moreover, we prove a similar type inequality for functions f∈Lq(Rn)∩W1,p(Rn) whenever 1<p<n and p<q≤p(n−1)n−p.

Quantitative Hardy inequalities for magnetic Hamiltonians

In this paper we present a new method of proof of Hardy type inequalities for two-dimensional quantum Hamiltonians with a magnetic field of finite flux. Our approach gives a quantitative lower bound on the best constant in these inequalities both for Schrödinger and Pauli operators. Pauli operators with Aharonov-Bohm magnetic field are discussed as well.