Social Sciences and Inequalities in the New Post-COVID-19 “Normal”

The pandemic caused by COVID-19 (either through its direct effects by the disease it causes or the measures taken in an attempt to control its spread) had, and still has, a profound effect at several levels beyond the medical, such as the economic and social, political, scientific, psychological, educational, legal and religious levels, among others. However, studies demonstrate that this influence has not been the same for all due to old inequalities and also the emergence of new inequalities. In this letter to the Editor, the authors discuss some of the contributions of the Social Sciences to the understanding of social inequalities in this new post-COVID-19 “normal” through the mobilization of relevant literature and also their experience in analysing COVID-19 with the eyes of the Social Sciences, notwithstanding their plurality. The results of this analysis allow concluding that the Social Sciences can make a very relevant contribution – in an interdisciplinary way – to the understanding of this phenomenon of the relationship between COVID-19 and inequalities based on socioeconomic factors with the aim of increasing social cohesion and social justice. Received: 4 October 2021 / Accepted: 11 November 2021 / Published: 3 January 2022

Inequalities for Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal Type f–Divergences

In this paper, we introduce new divergences called Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal in relation to convex functions. Some theorems, which give the lower and upper bounds for two new introduced divergences, are provided. The obtained results imply some new inequalities corresponding to known divergences. Some examples, which show that these are the generalizations of Rényi, Tsallis, and Kullback–Leibler types of divergences, are provided in order to show a few applications of new divergences.

Some New Reverse Hilbert’s Inequalities on Time Scales

This paper is interested in establishing some new reverse Hilbert-type inequalities, by using chain rule on time scales, reverse Jensen’s, and reverse Hölder’s with Specht’s ratio and mean inequalities. To get the results, we used the Specht’s ratio function and its applications for reverse inequalities of Hilbert-type. Symmetrical properties play an essential role in determining the correct methods to solve inequalities. The new inequalities in special cases yield some recent relevance, which also provide new estimates on inequalities of these type.

Pointwise monotonicity of heat kernels

In this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It deals with the monotonicity of the heat kernel from special points on revolution hypersurfaces. Our proof hinges on a non straightforward but elementary application of the parabolic maximum principle. As a consequence of the monotonicity property, we derive new inequalities involving classical special functions.

Some New Inequalities Using Nonintegral Notion of Variables

The object of this paper is to present an extension of the classical Hadamard fractional integral. We will establish some new results of generalized fractional inequalities.

Schur-Convexity for Elementary Symmetric Composite Functions and Their Inverse Problems and Applications

This paper investigates the Schur-convexity, Schur-geometric convexity, and Schur-harmonic convexity for the elementary symmetric composite function and its dual form. The inverse problems are also considered. New inequalities on special means are established by using the theory of majorization.

New inequalities for weaving frames in Hilbert spaces

In this paper, we establish Parseval identities and surprising new inequalities for weaving frames in Hilbert spaces which involve scalar $\lambda \in {\mathcal{R}}$ λ ∈ R . With suitable choices of λ, one obtains the previous results as special cases. Our results generalize and improve the remarkable results obtained by Balan et al. and Găvruţa.

Some new inequalities for convex functions via generalized integral operators and their applications

The authors discover an identity for a generalized integral operator via differentiable function. By using this integral equation, we derive some new bounds on Hermite–Hadamard type integral inequality for differentiable mappings that are in absolute value at certain powers convex. Our results include several new and known results as particular cases. At the end, some applications of presented results for special means and error estimates for the mixed trapezium and midpoint formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the field of integral inequalities.

Hermite–Hadamard-Type Inequalities for Generalized Convex Functions via the Caputo-Fabrizio Fractional Integral Operator

Due to applications in almost every area of mathematics, the theory of convex and nonconvex functions becomes a hot area of research for many mathematicians. In the present research, we generalize the Hermite–Hadamard-type inequalities for p , h -convex functions. Moreover, we establish some new inequalities via the Caputo-Fabrizio fractional integral operator for p , h -convex functions. Finally, the applications of our main findings are also given.