Aequationes Mathematicae最新文献

In this paper we consider some sufficient conditions for a function to be at most p-valent in the unit disc on the complex plane which are related to the known Ozaki’s and Noshiro-Warschawski conditions.

In this paper we investigate the functional equation

where ( I_1 , I_2 ) are open intervals of ( mathbb {R}), ( J = frac{1}{2} left( I_1 + I_2 right) ) moreover ( psi _1: I_1 rightarrow mathbb {R}), ( psi _2: I_2 rightarrow mathbb {R}) and ( varphi : J rightarrow mathbb {R}) are unknown functions. We describe the structure of the possible solutions assuming that ( varphi ) is measurable. In the case when ( varphi ) is a derivative, we give a complete characterization of the solutions. Furthermore, we present an example of a solution consisting of irregular Darboux functions. This provides the answer to an open problem proposed during the 59th International Symposium on Functional Equations.

Let S be a semigroup and K a field. Ebanks showed recently how the functional equation

where (g:S rightarrow K) denotes the unknown function and (x,y,z in S), is related to the sine addition law on S. We simplify Ebanks’ treatment. Furthermore we discuss for solutions (f,g:S rightarrow K) of the sine addition law the uniqueness of the component f given g, and we show that f and g are abelian, when (f ne 0).

Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming cubes there are unexpected relationships between many of these quantities. We obtain in particular formulas for the determinant of the distance matrix, the M-constant and the cofactor sum for such spaces. In general, these types of results offer valuable insights into the combinatorial optimization of certain constrained quadratic forms on finite metric spaces. A key focus in this context are embedding properties of negative type metrics, which play a prominent role in addressing important questions like the sparsest cut problem in graph theory. The current work extends previous results for unweighted metric trees, and more generally, for subsets of standard Hamming cubes, as well as results for weighted metric trees. Finally we consider polygonal equalities in these spaces, giving a complete description of the nontrivial 1-polygonal equalities that can arise in weighted Hamming cubes.

Let K be a convex body in ({mathbb {R}}^{n}). The Santaló point of K is the unique minimizer on ({textrm{int}}(K)) of the function (umapsto {textrm{vol}}_{textrm{n}} ((K-u)^{circ })), where (Q^{circ }) denotes the polar convex body of Q and “({textrm{vol}}_n)” is the n-dimensional volume. In a sense, the Santaló point plays the role of a central point of K. This work studies a variant of such a concept of centrality: we change volume by diameter. The theory of “diametral” Santaló points diverges from the classical theory in a number of ways.

This paper introduces and analyzes some new highly efficient iteration procedures for approximating fixed points of contractive-type mappings. The stability, strong convergence, and performance of the proposed schemes have been investigated through numerical examples. Numerical examples demonstrate that the newly introduced schemes produce highly accurate approximations comparable to other similar robust schemes appeared in the literature. Nevertheless, all the schemes developed here are more efficient than similar robust schemes available in the literature.

In this research, the main attention is given to positive and alternating Lüroth series, as well as to differential, integral, and other properties of certain functions defined by these series.

The aim of this paper is to study the fractional maximal commutators (M_{b,alpha }) and the commutators of the fractional maximal operator ([b, M_{alpha }]) in the total Morrey spaces (L^{p,lambda ,mu }(mathbb {G})) on any stratified Lie group (mathbb {G}) when b belongs to Lipschitz spaces (dot{Lambda }_{beta }(mathbb {G})). Some new characterizations for certain subclasses of Lipschitz spaces (dot{Lambda }_{beta }(mathbb {G})) are given.

We discuss the question of compatibility of some indices used by the United Nations Development Program to determine the level of human development. Our goal is to restrict the range of arbitrariness in choosing quasi-arithmetic means to measure the development in different countries. As our main tool we use functional equations.

The isoperimetric problem for hyperbolic hyperideal pyramids is studied. The pyramid corresponding to a critical point of the volume function uniquely maximizes the volume among hyperideal pyramids with the same type and surface area. The conditions for the existence of a critical point in the domain are also established.