Volume 75, Issue 6

The aim of this paper is to give a categorical equivalence for Stone algebras. We introduce the variety of Stone-Kleene algebras with intuitionistic negation, or Stone KAN-algebras for short, and explore Kalman’s construction for Stone algebras. We examine the centered algebras within this new variety and prove that the category of Stone algebras is equivalent to the category of centered Stone KAN-algebras. Moreover, inspired by Monteiro’s construction for Nelson algebras, we propose a method to construct a centered Stone KAN-algebra from a given Stone KAN-algebra and show the connection between Kalman’s construction and Monteiro’s construction.

In this paper, a new concept called J -prime filters in BL-algebras are investigated. A J -prime filter F is defined as a proper filter that preserves the property of being prime with respect to another filter J . If J is not a subset of F , then the J -prime filter is referred to as an NJ -prime filter. The relationships between these filters and their connections to minimal prime filters and maximal filters are investigate.

Recently, P. Das, A. Ghosh and T. Aziz have given a criterion for statistically characterized subgroups of the circle group ℝ/ℤ to be torsion. Here we give a completely different and much shorter proof of this result. Moreover, we give for a characterized subgroup of ℝ/ℤ a sufficient condition to be torsion, unifying and generalizing earlier results.

This article presents new results that extend the scope of the Young integral inequality. They are formulated by different functional composition schemes of the integrals involved. These schemes depend on a unique auxiliary function. In total, six theorems are proved. Four of them are derived from a simple composition scheme based on sub-additive, super-additive, convex and concave properties of the auxiliary function, while the remaining two use more sophisticated composition schemes based on convex and concave properties. Our framework also unifies several established variants of the Young integral inequality. Three secondary propositions complete the theorems. The theory is supported by a number of tractable examples involving power, exponential, logarithmic, ratio and hyperbolic functions.

The characterization of pseudo- n -uninorms with continuous underlying functions, i.e., the non-commutative version of n -uninorms, where all underlying (pseudo-)t-norms and (pseudo-)t-conorms are continuous, is discussed. The structure of an n -uninorm, which can be decomposed by the z -ordinal sum and the structure of a pseudo- n -uninorm, which cannot be decomposed by this approach, in general, are compared. It is shown that any pseudo- n -uninorm with continuous underlying functions can be decomposed via non-commutative ordinal sum into trivial and representable summands.

Extension for Jensen-type inequality and reverse of Jensen’s inequality under the assumption of second-order differential inequality p(x)f(x)+q(x)f′(x)+f′′(x)≥0$$ \begin{equation*}p(x)f(x)+q(x)f^{\prime}(x)+f^{\prime\prime}(x)\ge 0 \end{equation*}$$ are established, Hermite–Hadamard-type inequality is also proven. We get some refinements of power mean inequality as applications and further extend normalised Jensen functional under the assumption of second-order differential inequality as an improvement.

This article presents the first self-contained and direct proof of a widely recognized result that the discrete Choquet integral, when defined from a discrete fuzzy measure (or capacity), is convex if and only if the discrete fuzzy measure itself is submodular. In contrast to existing proofs, our argument is constructed directly from the fuzzy measure defined on a finite set, employing only standard techniques from the theory of capacities and Choquet integration.

This paper aims to study the complex Monge-Ampère measure of an envelope of 𝓕-plurisubharmonic functions. As an application, we prove the existence of a solution to the complex Monge-Ampère type equation in bounded 𝓕-hyperconvex domains.

In this paper, we establish the sharp Fekete-Szegö inequalities of functional type over a new class of holomorphic mappings on the unit disk in a complex plane. This class includes some significant widely studied classes. Further, we develop an method to extend our result to higher dimensions. The main theorems of this paper provide a generalization of the Fekete-Szegö coefficients problems for some known classes.

In the paper, using the idea of normal family, we investigate the uniqueness problem of entire functions that share two values partially with their k -th derivatives. The obtained results improve the results of Lü, Xu and Yi (Ann. Polon. Math. 95(1) (2009), 67–75) in a large scale. Also, as an application of our results, we have settled the conjecture posed by Li and Yang (Illinois J. Math. 44(2) (2000), 349–362).

This paper examines the oscillatory behavior of a class of third-order semi-canonical nonlinear delay dynamic equations a(ℓ)r(ℓ)ϰΔ(ℓ)ΔαΔ+q(ℓ)ϰβ(℘(ℓ))=0. $$ \begin{equation*}\left( a(\ell) \left[\left(r(\ell) \varkappa^{\Delta} (\ell) \right)^{\Delta} \right]^{\alpha} \right)^{\Delta} + q(\ell) \varkappa^{\beta}(\wp(\ell))=0. \end{equation*}$$ The core objective is to streamline the analysis of the non-oscillatory solutions by converting the semi-canonical operator to an equivalent canonical form. This transformation facilitates the derivation of novel oscillation results by establishing criteria for the non-existence of non-oscillatory solutions. The practical examples provided in this paper illustrate the novelty of our findings, which contribute to enhancing, generalizing, and extending the existing literature.

In the Korovkin-type approximation, more stronger results can be obtained by using the matrix summability method compared to the classical results in the literature. One of these summability methods, weighted B -summability, was defined by Mohiuddine in 2016 as the weighted summability of the B -transform of a sequence x to a number L . In this paper, we give a Korovkin-type theorem using the notion of weighted B -summability for sequences of positive linear operators on weighted spaces. We also study the rates of convergence of these operators.

We consider the classical double convolution product and the Duhamel product for functions in two variables and study their some properties and applications. Namely, we investigate *-generators of the Banach algebra Cxy(n):=f∈Cnt[0,1]×t[0,1]:f(x,y)=g(xy)for someg∈Ct[0,1](n). $$C^{(n)}_{xy}:=\left\{f\in C^{n}\left(t[0,1]\times t[0,1]\right) :f(x,y)=g(xy)\,\,\text{for some}\,\,g\in C^{(n)}_{t[0,1]}\right\} . $$ Also we describe the maximal ideal space of the Banach algebra (Cxy(n),⊛) $ (C^{(n)}_{xy},\circledast) $ with respect to the Duhamel product ⊛ defined by (f⊛g)(x,y)=∂2∂x∂y∫0x∫0yf(x−t)(y−τ)g(tτ)dτdt. $$(f\circledast g)(x,y)=\frac{\partial^{2}}{\partial x\partial y} \int \limits_{0}^{x}\int \limits_{0}^{y} f(x-t)(y-\tau)g(t\tau)\text{d}\tau\, {\text{d}} t. $$

Given an F -space ( X, τ ) and σ ≤ τ a linear topology on X , this paper provides the definition of a general set function that allows us to define measures of σ -noncompactness in X . In particular, we construct measures of nonconvex σ -noncompactness that are monotonic, invariant under passage to the closed convex hull, and satisfy the Cantor intersection property. Additionally, we derive a fixed point theorem for maps that satisfy the classical Darbo condition with respect to a given measure of nonconvex σ -noncompactness.

This paper proves that if the sufficient condition for the Kolmogorov–Feller–Gut weak law of large numbers is satisfied, then the corresponding sequence of partial sums converges in mean. The underlying random variables are only assumed to be pairwise negatively dependent. The proof is based on a von Bahr–Esseen-type inequality for pairwise negatively dependent random variables and some properties of regularly varying functions. The main theorems strengthen several results in the literature.

The work of this paper is devoted to obtaining strong laws for intermediately trimmed sums of random variables with infinite means. Particularly, we provide conditions under which the intermediately trimmed sums of independent but not identically distributed random variables converge almost surely. Moreover, by dropping the assumption of independence we provide a corresponding convergence result for a special class of Oppenheim expansions. We highlight that the results of this paper generalize the results provided in the recent work of [13] while the convergence of intermediately trimmed sums of generalized Oppenheim expansions is studied for the first time.

Weighted distributions play an important role in reliability and engineering. This research contributes to the topic by presenting a novel flexible two-parameter weighted distribution characterized by extensive statistical properties. Various parameter estimation methods are also thoroughly investigated. Their effectiveness is validated by complete simulation studies. Within the framework of generalized linear models, a regression model is established for positively defined response variables. Two data sets are examined to emphasize the importance of the proposed model. In addition, the WBreg tool is presented to facilitate its use by researchers. WBreg is available “free of charge” at https://beststat.shinyapps.io/WB2reg .

In this paper, we introduce a new q -Gamma probability distribution which is an extension of the classical Gamma distribution in the context of q -calculus. It is also a generalization of the q -exponential distribution. The main properties of the proposed model are presented. Its non-centered moments of any order were explicitly computed. In particular, the kurtosis and skewness were explicitly determined. Moreover, the maximum-likelihood estimation method of the parameters was developped. The performance of the estimation approach as well as the Metropolis-Hastings-based generation method were studied through several numerical experiments. In addition, a characterization of the q -exponential distribution is established using the truncated moments.

In this article we consider two categories: the category of finiteorthoatomistic effect algebras and the category of regular algebraic E -test spaces. S. Gudder introduced (algebraic) E -test spaces and showed that for each algebraic E -test space ( X; 𝒯 ) there exists an effect algebra Π( X ). Moreover Π is a covariant functor from the category of algebraic E -test spaces to the category of effect algebras. We show that the category of regular and algebraic E -test spaces is equivalent to the category of finiteorthoatomistic effect algebras. We proved that atoms in effect algebras corresponding to regular and algebraic E -test spaces are perspectivity classes of characteristic functions of one-element sets. We found an example of algebraic E -test space which is not regular and in corresponding E -test space some perspectivity class of the characteristic function of a singleton is not an atom.