Mathematics and music game in the function of child’s social and emotional development

The paper presents empirical research, aiming to present the extent to which the application of the concrete mathematical and musical play contributes to the child’s social and emotional development. The research was conducted in two international schools in Belgrade, using the play titled ‘Musical Monkeys’ and in collaboration with the Music-Math team from Mexico who are the creators of the mentioned game. The results have shown that this kind of approach in working with children encourages activity and engagement, self-confidence, empathy, team work, integrity, tolerance and enthusiasm, while requiring and encouraging collaboration and constructive communication, cooperation and respect among students in the process of solving a set of mathematical and/ or musical tasks. The obtained results confirm that the children established connection between the mathematical and musical segments involving a high level of emotional and social skills – collaboration, communication, empathy, enthusiasm, commitment, curiosity for the game and felt benefits of team work, tolerance and respect while solving the given educational tasks

On the Distribution of Kurepa’s Function

Kurepa’s function and his hypothesis have been investigated by means of numerical simulation. Particular emphasis has been given to the conjecture on its distribution, that should be one of a random uniform distribution, which has been verified for large numbers. A convergence function for the two has been found

Harmonic quasiconformal mappings and hyperbolic type metrics

The book presents a research area in geometric function theory concerned with harmonic quasiconformal mappings and hyperbolic type metrics defined on planar and multidimensional domains. The classes of quasiconformal and quasiregular mappings are well established areas of study in this field as these classes are natural and fruitful generalizations of the class of analytic functions in the planar case. The book contains many concrete examples, as well as detailed proofs and explanations of motivations behind given results, gradually bringing the reader to the forefront of current research in the area. This monograph was written for a wide readership from graduate students of mathematical analysis to researchers working in this or related areas of mathematics who want to learn the tools or work on open problems listed in various parts of the book

Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities

In this article, we give sharp two-sided bounds for the generalized Jensen functional Jn(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean An(h;p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Hölder’s inequality are obtained

Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities

In this article, we give sharp two-sided bounds for the generalized Jensen functional Jn(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean An(h;p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Hölder’s inequality are obtained

Remarks on Recent Results for Generalized <i>F</i>-Contractions

In this paper, we give some remarks on the recent papers on generalized F-contractions. Our results unify and generalize the previous results in the existing literature. Moreover, we give an example to support our results. As an application, we give the existence and uniqueness of a solution to a class of differential equations

Remarks on Recent Results for Generalized F-Contractions

In this paper, we give some remarks on the recent papers on generalized F-contractions. Our results unify and generalize the previous results in the existing literature. Moreover, we give an example to support our results. As an application, we give the existence and uniqueness of a solution to a class of differential equations

Drugačiji pristup prema b(αn,βn)-hipermetričkim prostorima

Introduction/purpose: The aim of this paper is to present the concept of b(an,bn)-hypermetric spaces. Methods: Conventional theoretical methods of functional analysis. Results: This study presents the initial results on the topic of b(an,bn)-hypermetric spaces. In the first part, we generalize an n-dimensional (n ≥ 2) hypermetric distance over an arbitrary non-empty set X. The b(an,bn)-hyperdistance function is defined in any way we like, the only constraint being the simultaneous satisfaction of the three properties, viz, non-negativity and positive-definiteness, symmetry and (an, bn)-triangle inequality. In the second part, we discuss the concept of (an, bn)-completeness, with respect to this b(an,bn)-hypermetric, and the fixed point theorem which plays an important role in applied mathematics in a variety of fields. Conclusion: With proper generalisations, it is possible to formulate well-known results of classical metric spaces to the case of b(an,bn)-hypermetric spaces.Uvod/cilj: Cilj ovog rada jeste da se predstavi koncept b(αn,βn)-hipermetričkih prostora. Metode: Primenjene su konvencionalne teoretske metode funkcionalne analize. Rezultati: U radu su predstavljeni inicijalni rezultati koji se odnose na b(αn,βn)-hipermetričke prostore. U prvom delu generalizuje se n-dimenzionalno (n ≥ 2) hipermetričko rastojanje na proizvoljnom nepraznom skupu X. Funkcija b(αn,βn)-hiperrastojanja može se definisati na proizvoljan način dokle God su zadovoljene tri osobine: nenegativnost, pozitivna definitnost, simetrija i (αn,βn)-nejednakost trougla. U drugom delu rada razmatrani su koncept (αn,βn)-kompletnosti u odnosu na b(αn,βn) )-hipermetriku i teorema fiksne tačke, koja ima značajnu ulogu u primenjenoj matematici na više polja. Zaključak: Odgovarajućim generalizacijama moguće je formulisati poznate rezultate klasičnih metričkih prostora na slučaj b(αn,βn)-hipermetričkih prostora

Fixed Point Results via <inline-formula><math display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-Transitive Binary Relation and Fuzzy <inline-formula><math display="inline"><semantics><mi mathvariant="script">L</mi></semantics></math></inline-formula>-<inline-formula><math display="inline"><semantics><mi mathvariant="script">R</mi></semantics></math></inline-formula>-Contraction

In this study, we initiate the concept of fuzzy L-R-contraction and establish some fixed point results involving a G-transitive binary relation and fuzzy L-simulation functions, by employing suitable hypotheses on a fuzzy metric space endowed with a binary relation. The presented results unify, generalize, and improve various previous findings in the literature