Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas 

About: Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Mathematics & Banach space. It has an ISSN identifier of 1578-7303. Over the lifetime, 1503 publications have been published receiving 11328 citations. The journal is also known as: RACSAM & Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales / A.

Relative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the analytic hierarchy/network process

Abstract: According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish measurements for intangible properties that have no scales of measurement. In that case the value derived for each element depends on what other elements it is compared with. We show how relative scales can be derived by making pairwise comparisons using numerical judgments from an absolute scale of numbers. Such measurements, when used to represent comparisons can be related and combined to define a cardinal scale of absolute numbers that is stronger than a ratio scale. They are necessary to use when intangible factors need to be added and multiplied among themselves and with tangible factors. To derive and synthesize relative scales systematically, the factors are arranged in a hierarchic or a network structure and measured according to the criteria represented within these structures. The process of making comparisons to derive scales of measurement is illustrated in two types of practical real life decisions, the Iran nuclear show-down with the West in this decade and building a Disney park in Hong Kong in 2005. It is then generalized to the case of making a continuum of comparisons by using Fredholm’s equation of the second kind whose solution gives rise to a functional equation. The Fourier transform of the solution of this equation in the complex domain is a sum of Dirac distributions demonstrating that proportionate response to stimuli is a process of firing and synthesis of firings as neurons in the brain do. The Fourier transform of the solution of the equation in the real domain leads to nearly inverse square responses to natural influences. Various generalizations and critiques of the approach are included.

Optimality Results for Dividend Problems in Insurance

Abstract: This paper is a survey of some classical contributions and recent progress in identifying optimal dividend payment strategies in the framework of collective risk theory. In particular, available mathematical tools are discussed and some challenges are described that occur under various objective functions and model assumptions. Finally, some open research problems in this field are stated.

Monotonicity and convexity involving generalized elliptic integral of the first kind

Abstract: In this paper, we present the monotonicity properties of the ratio between generalized elliptic integral of the first kind $${\mathcal {K}}_a(r)$$ and its approximation $$\log [1+2/(ar')]$$ , and also the convexity (concavity) of their difference for $$a\in (0,1/2]$$ . As an application, we give new bounds for generalized Grotzsch ring function $$\mu _a(r)$$ and a upper bound for $${\mathcal {K}}_a(r)$$ .

Convexity and concavity of the modified Bessel functions of the first kind with respect to Hölder means

Abstract: In this paper, we establish a necessary and sufficient condition for the convexity and concavity of the modified Bessel functions of the first kind with respect to Holder means.

Various generalizations of metric spaces and fixed point theorems

Abstract: There have been many attempts to generalize the definition of a metric space in order to obtain possibilities for more general fixed point results. In this paper, we give a survey of recent results on reducing fixed point theorems on generalized metric spaces to fixed point theorems on metric spaces and then investigate this fact in other generalized metric spaces. We show that many generalized metric spaces are topologically equivalent to certain metric spaces or to previously generalized metric spaces. Also, the fixed point theory in these generalized metric spaces may be a consequence of the fixed point theory in certain metric spaces or in previously generalized metric spaces.