Generalized Cauchy means

Given two means M and N, the operator MM,NMM,N assigning to a given mean μ the mean MM,N(μ)(x,y)=M(μ(x,N(x,y)),μ(N(x,y),y)) was defined in Berrone and Moro (Aequationes Math 60:1–14, 2000) in connection with Cauchy means: the Cauchy mean generated by the pair f, g of continuous and strictly monotonic functions is the unique solution μ to the fixed point equation MA(f),A(g)(μ)=μ, where A(f) and A(g) are the quasiarithmetic means respectively generated by f and g. In this article, the operator MM,NMM,N is studied under less restrictive conditions and a general fixed point theorem is derived from an explicit formula for the iterates MnM,NMM,Nn . The concept of class of generalized Cauchy means associated to a given family of mixing pairs of means is introduced and some distinguished families of pairs are presented. The question of equality in these classes of means remains a challenging open problem.Fil: Berrone, Lucio Renato. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems

Sufficient conditions are obtained for a Volterra integral equation whose kernel depends on an increasing parameter a to admit an approximation of the identity with respect to a in the form of a resolvent kernel. In this case, the solution of the integral equation tends to zero as a tends to infinity, and we establish estimates of this convergence in L. These results are used for obtaining estimates of the convergence of linear heat-transfer boundary conditions to Dirichlet ones as the heat-transfer coefficient tends to infinity.Отримані достатні умови, при яких інтегральне рівняння Вольтерра з ядром, що залежить від зростаючого параметра α, допускає наближення одиниці відносно α у вигляді резольвентного ядра. У цьому випадку розв'язок інгегрального рівняння прямує до нуля, коли а прямує до нескінченності, і отримані оцінки цієї збіжності в L∞. За допомогою цих результатів одержані оцінки збіжності лінійних граничних умов Діріхле, коли коефіцієнт теплообміну прямує до нескінченності

The Aumann functional equation for general weighting procedures

The functional equation of composite type M(M(x; M(x; y)); M(M(x; y); y)) = M(x; y) arose in the course of the studies on the problem of extension and restriction of the number of arguments of a mean M performed by G. Aumann at the third decade of the past century. A solution to (1) in the analytic case was ulteriorly obtained by Aumann himself and remained as a noteworthy characterization of analytic quasiarithmetic means. An ample generalization of equation (1) which involves general weighting operators is considered in this paper. Under mild conditions on the regularity of the involved means, the general solution to this generalized equation is obtained for a particularly tractable class of weighting operators.Fil: Berrone, Lucio Renato. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingenieria y Agrimensura. Escuela de Ingenieria Electrónica. Laboratorio de Acústica y Electroacústica; Argentin

P-means and the solution of a functional equation involving Cauchy differences

Solutions to the functional equation f(x+y)−f(x)−f(y)=2f(Φ(x,y)),x,y>0, are sought for the admissible pairs (f,Φ)(f,Φ) constituted by a strictly monotonic function f and a strictly increasing in both variables mean ΦΦ . A related class of means, P-means, is introduced, studied and then employed in solving (1) under additional hypotheses on ΦΦ . For instance, Ger has proved that the unique P-mean which is also quasiarithmetic is the geometric mean G(x,y)=xy−−√G(x,y)=xy . An elementary proof to this result is given in this paper. Moreover, as a consequence of a fundamental result on the uniqueness of representation of P-means it is proved that the geometric mean G is the unique homogeneous P-mean.Fil: Berrone, Lucio Renato. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingenieria y Agrimensura. Escuela de Ingenieria Electrónica. Laboratorio de Acústica y Electroacústica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentin

Family firms going international: Integrating corporate identity‐building processes and socioemotional wealth dimensions

This study aims to improve understanding of how identity-building processes shape corporate identity and how dimensions of socioemotional wealth affect internationalization pathways in a family firm. The paper uses an in-depth case study of an Italian family firm internationally recognized as excellent in its industry. We developed an integrative theoretical model, combining socioemotional wealth frameworks and elements of the corporate identity mix. This enabled us to incorporate more theoretical knowledge from the field of international management into the domain of family business research. The latent construct of socioemotional wealth provides an in-depth understanding of the multidimensional nature of corporate identity-building processes and shows the intertwined nature of corporate identity and the "affective endowment" in the development of internationalization strategies