ACTA SCIENTIARUM MATHEMATICARUM最新文献

The basis for our studies is a large class of orthogonal polynomial sequences ((P_n)_{nin {{mathbb {N}}}_0}), which is normalized by (P_n(x_0)=1) for all (nin {mathbb {N}}_0) where the coefficients in the three-term recurrence relation are bounded. The goal is to check if (x_0 in {mathbb {R}}) is in the support of the orthogonalization measure (mu ). For this purpose, we use, among other things, a result of G. H. Hardy concerning Cesàro operators on weighted (l^2)-spaces. These investigations generalize ideas from Lasser et al. (Arch Math 100:289–299, 2013).

Power difference means and Heron means are well-known numerical means with parameters. Their comparison in the positive definite sense is studied. More precisely, for a power difference mean M with each fixed parameter we try to determine the exact parameter range for Heron means majorizing M (in the positive definite sense). Since this order is known to determine validity of (unitarily invariant) norm inequalities between corresponding matrix power difference means and matrix Heron means, we obtain an abundance of very precise norm inequalities between these two matrix means.

In this paper, we establish and study some properties of the spatial numerical range of right linear bounded operators on a right quaternionic Banach space. To be more specific, we show that the spatial numerical range is circular and we give the relation between the spatial numerical range, the point S-spectrum and the approximate S-spectrum of an operator on a right quaternionic Banach space. We prove also that the S-spectrum of a quaternionic bounded operator is included in the closure of its spatial numerical range. To show this, we generalize the Bishop-Phelps theorem for quaternionic Banach spaces.

We introduce a weaker form of continuity which is a necessary and sufficient condition for the existence of fixed points. The obtained theorems exhibit interesting fixed point – eventual fixed point patterns. If we slightly weaken the conditions then the mappings admit periodic points besides fixed points and such mappings possess interesting combinations of fixed and periodic points. Our results are applicable to contractive type as well as non-expansive type mappings. Our theorems are independent of almost all the existing results for contractive type mappings. The last theorem of Sect. 2 is applicable to mappings having various geometric patterns as their domain and is perhaps the first result of its type that also opens up scope for the study of periodic points and periodic point structures. We also give an application of our theorem to obtain the solutions of a nonlinear Diophantine equation; and also show that various well-known fixed point theorems are not applicable in solving this equation.

In this paper, we introduce and investigate a new class of operators known as almost unbounded L-weakly compact (in shortly, (_{au}L)-weakly compact) and almost unbounded M-weakly compact (in shortly, (_{au}M)-weakly compact) operators. We explore the lattice properties related to this class and examine their relationships with other established operator classes, such as L-weakly compact operators and almost L-weakly compact operators. We demonstrate that every L-weakly compact operator is an (_{au}L)-weakly compact operator, but the reverse implication does not necessarily hold in all cases.

Let (G=(V,E)) be a finite graph together with an initial assignment (Vrightarrow {0,1}) that represents the opinion of each vertex. Then discordant push voting is a discrete, non-deterministic protocol that alters the opinion of one vertex at a time until a consensus is reached. More precisely, at each round a discordant vertex u (i.e., one that has a neighbor with a different opinion) is chosen uniformly at random, and then we choose a neighbor v with different vote uniformly at random, and force v to change its opinion to that of u. In case of the discordant pull protocol we simply choose a discordant vertex uniformly at random and change its opinion. In this paper, we give asymptotically sharp estimations for the worst expected runtime of the discordant push and pull protocols on the star graph.

In this article we study log-majorizations related to the spectral geometric and Rényi means. Our goal is to establish certain geometric properties for them with respect to the Thompson metric and Kim’s semi-metric on the cone of positive definite matrices. We also study geodesic in-betweenness type results for these two means and some Audenaert-type in-betweenness inequalities.

The Lebesgue differentiation theorem claims that the integral averages of (fin L^{1}([0,1)^2)) with respect to the family of axis-parallel squares converge almost everywhere on ([0,1)^2). On the other hand, it is a well known result by Saks that there exist a function (f in L^{1}([0,1)^2)) such that its integral averages with respect to the family of axis-parallel rectangles diverge everywhere on ([0,1)^2). In this paper, we address the following question: assume we have two different collections of rectangles; under which conditions does there exist a function (f in L^{1}([0,1)^2)) so that its integral averages converge with respect to one collection and diverge with respect to another? More specifically, let ({varvec{C}}, {varvec{D}} subset (0,1]) and consider rectangles with side lengths respectively in ({varvec{C}}) and ({varvec{D}}). We show that if the sets ({varvec{C}}) and ({varvec{D}}) occasionally become sufficiently “far” from each other, then such a function can be constructed. We also show that in the class of positive functions our condition is necessary for such a function to exist.

This paper delves into the examination of algebraic and topological attributes associated with the domains (c_0(G,q)), c(G, q), and (ell _infty (G,q)) pertaining to the Lambda–Pascal matrix G in Maddox’s spaces (c_0(q)), c(q), and (ell _infty (q)), respectively. The determination of the Schauder basis and the computation of (alpha )-, (beta )-, and (gamma )-duals for these Lambda–Pascal paranormed spaces are carried out. The ultimate section is dedicated to elucidating the classification of the matrix classes ((ell _{infty }(G,q),ell _{infty })), ((ell _{infty }(G,q),f)), and ((ell _{infty }(G,q),c)), concurrently presenting the characterization of specific other sets of matrix transformations in the space (ell _{infty }(G,q)) as corollaries derived from the primary outcomes.

A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of Adaricheva and Bolat (Discrete Math 342(N3):726–746, 2019) and the Polymath REU 2020 team (Convex geometries representable by at most 5 circles on the plane. arXiv:2008.13077), continues to investigate representations of convex geometries on a 5-element base set. It introduces several properties: the opposite property, nested triangle property, area Q property, and separation property, of convex geometries of circles on a plane, preventing this representation for numerous convex geometries on a 5-element base set. It also demonstrates that all 672 convex geometries on a 5-element base set have a representation by ellipses, as given in the appendix for those without a known representation by circles, and introduces a method of expanding representation with circles by defining unary predicates, shown as colors.