Proyecciones (Antofagasta, On line) <p align="justify">La revista&nbsp;Proyecciones. Journal of Mathematics es una publicación científica, sin fines de lucro, oficial de la Universidad Católica del Norte, Antofagasta, Chile. Fue fundada en 1982 y depende del Departamento de Matemáticas de la Universidad Católica del Norte.<br>Proyecciones. Journal of Mathematics edita un volumen con 5 números al año.</p> Universidad Católica del Norte. en-US Proyecciones (Antofagasta, On line) 0717-6279 Stability, boundedness and existence of unique periodic solutions to a class of functional differential equations <p><em>In this paper a novel class of fourth order functional differential equations is discussed. By reducing the fourth order functional differential equation to system of first order, a suitable complete Lyapunov functional is constructed and employed to obtain sufficient conditions that guarantee existence of a unique periodic solution, asymptotic and uniform asymptotic stability of the zero solutions, uniform boundedness and uniform ultimate boundedness of solutions. The obtained results are new and include many prominent results in literature. Finally, two examples are given to show the feasibility and reliability of the theoretical results. </em></p> Adeleke Timothy Ademola Copyright (c) 2021 Adeleke Timothy Ademola 2021-02-16 2021-02-16 40 2 271 303 10.22199/issn.0717-6279-2021-02-0017 On the maximal invariant set for the map X² - 2 restricted to intervals <p><em>In this paper, we study the maximal invariant set of a quadratic family related to a class of unimodal maps. This family is very important and have direct application in many branches of science. In particular, we characterize when the maximal invariant of f(x) = x<sup>2</sup> − 2 (restricted to an interval) has a chaotic behavior. </em></p> Dušan Bednařík Diego Marques Carlos Gustavo Tamm de Araujo Moreira Pavel Trojovský Copyright (c) 2021 Dušan Bednařík, Diego Marques, Carlos Gustavo Tamm de Araujo Moreira, Pavel Trojovský 2021-02-16 2021-02-16 40 2 305 312 10.22199/issn.0717-6279-2021-02-0018 On the three families of extended Laguerre-based Apostol-type polynomials <p><em>In this paper, we introduce a new class of generalized extended Laguerre-based Apostol-type-Bernoulli, Apostol-type-Euler and Apostoltype-Genocchi polynomials. These Apostol type polynomials are used to connect Fubini-Hermite and Bell-Hermite polynomials and to find new representations. We derive some implicit summation formulae and symmetric identities for these families of special functions by applying the generating functions.</em></p> M. A. Pathan Waseem A. Khan Copyright (c) 2021 M. A. Pathan, Waseem A. Khan 2021-02-16 2021-02-16 40 2 313 334 10.22199/issn.0717-6279-2021-02-0019 A study of topological structures on equi-continuous mappings <p><em>Function space topologies are developed for EC(Y,Z), the class of equi-continuous mappings from a topological space Y to a uniform space Z. Properties such as splittingness, admissibility etc. are defined for such spaces. The net theoretic investigations are carried out to provide characterizations of splittingness and admissibility of function spaces on EC(Y,Z). The open-entourage topology and pointtransitive-entourage topology are shown to be admissible and splitting respectively. Dual topologies are defined. A topology on EC(Y,Z) is found to be admissible (resp. splitting) if and only if its dual is so.</em></p> <p><em> </em></p> Ankit Gupta Ratna Dev Sarma Copyright (c) 2021 Ankit Gupta, Ratna Dev Sarma 2021-02-16 2021-02-16 40 2 335 354 10.22199/issn.0717-6279-2021-02-0020