Proyecciones (Antofagasta, On line) 2021-02-16T00:00:00+00:00 Ricardo Soto Montero Open Journal Systems <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> Stability, boundedness and existence of unique periodic solutions to a class of functional differential equations 2020-05-13T16:37:12+00:00 Adeleke Timothy Ademola <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> 2021-02-16T00:00:00+00:00 Copyright (c) 2021 Adeleke Timothy Ademola On the maximal invariant set for the map X² - 2 restricted to intervals 2020-01-03T12:59:49+00:00 Dušan Bednařík Diego Marques Carlos Gustavo Tamm de Araujo Moreira Pavel Trojovský <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> 2021-02-16T00:00:00+00:00 Copyright (c) 2021 Dušan Bednařík, Diego Marques, Carlos Gustavo Tamm de Araujo Moreira, Pavel Trojovský On the three families of extended Laguerre-based Apostol-type polynomials 2020-05-02T00:27:11+00:00 M. A. Pathan Waseem A. Khan <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> 2021-02-16T00:00:00+00:00 Copyright (c) 2021 M. A. Pathan, Waseem A. Khan A study of topological structures on equi-continuous mappings 2020-10-10T20:01:52+00:00 Ankit Gupta Ratna Dev Sarma <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> 2021-02-16T00:00:00+00:00 Copyright (c) 2021 Ankit Gupta, Ratna Dev Sarma Lacunary sequences of complex uncertain variables defined by Orlicz functions 2020-02-19T19:01:37+00:00 Pranab Jyoti Dowari Binod Chandra Tripathy <p><em>Using the concept of Orlicz function and uncertainty theory, some new class of lacunary convergent sequences defined by Orlicz functions have been introduced with the lacunary convergence concepts in this paper. Some topological properties of the defined sequence spaces along with the inclusion relations have been investigated.</em></p> 2021-03-01T00:00:00+00:00 Copyright (c) 2021 Pranab Jyoti Dowari, Binod Chandra Tripathy On ideal sumset labelled graphs 2020-02-21T20:51:25+00:00 Jincy P. Mathai Sudev Naduvath Satheesh Sreedharan <p><em>The sumset of two sets A and B of integers, denoted by A + B, is defined as A+B = {a+b : a </em><em>∈</em><em> A, b </em><em>∈</em><em> B}. Let X be a non-empty set of non-negative integers. A sumset labelling of a graph G is an injective function </em><em>f</em><em> : V (G) → P(X) − {</em><em>∅</em><em>} such that the induced function </em><em>f<sup>+</sup></em><em> : E(G) → P(X)−{</em><em>∅</em><em>} is defined by </em><em>f+</em><em>(uv) = </em><em>f</em><em>(u) +</em><em>f</em><em>(v) </em><em>∀</em><em>uv </em><em>∈</em><em> E(G). In this paper, we introduce the notion of ideal sumset labelling of graph and discuss the admissibility of this labelling by certain graph classes and discuss some structural characterization of those graphs.</em></p> 2021-03-01T00:00:00+00:00 Copyright (c) 2021 Jincy P. Mathai, Sudev Naduvath, Satheesh Sreedharan On independent position sets in graphs 2020-04-04T16:03:58+00:00 Elias John Thomas Ullas Chandran S. V. <p><em>An independent set S of vertices in a graph G is an independent position set if no three vertices of S lie on a common geodesic. An independent position set of maximum size is an ip-set of G. The cardinality of an ip-set is the independent position number, denoted by ip(G). In this paper, we introduce and study the independent position number of a graph. Certain general properties of these concepts are discussed. Graphs of order n having the independent position number 1 or n − 1 are characterized. Bounds for the independent position number of Cartesian and Lexicographic product graphs are determined and the exact value for Corona product graphs are obtained. Finally, some realization results are proved to show that there is no general relationship between independent position sets and other related graph invariants </em></p> 2021-03-01T00:00:00+00:00 Copyright (c) 2021 Elias John Thomas, Ullas Chandran S. V. Some remarks on fuzzy infi topological spaces 2020-05-26T07:25:09+00:00 Birojit Das Baby Bhattacharya Apu Kumar Saha <p><em>Induced fuzzy infi topological space is already introduced by Saha and Bhattacharya [Saha A.K., Bhattacharya D. 2015, Normal Induced Fuzzy Topological Spaces, Italian Journal of Pure and Applied Mathematics, 34, 45-56]. In this paper for the said space, we further analyse some properties viz. fuzzy I-continuity, fuzzy infi open mappings and fuzzy infi closed mappings etc. Also we study product fuzzy infi topological space and establish some results concerned with it.</em></p> 2021-03-01T00:00:00+00:00 Copyright (c) 2021 Birojit Das, Baby Bhattacharya, Apu Kumar Saha Implicative filters in quasi-ordered residuated system 2020-05-04T17:37:13+00:00 Daniel Romano <p><em>The concept of residuated relational systems ordered under a quasiorder relation was introduced in 2018 by S. Bonzio and I. Chajda as a structure </em><em>𝒜</em><em> = </em><em>〈</em><em>A, ·,→, 1, R</em><em>〉</em><em>, where (A, ·) is a commutative monoid with the identity 1 as the top element in this ordered monoid under a quasi-order R. The author introduced and analyzed the concepts of filters in this type of algebraic structures. In this article, as a continuation of previous author’s research, the author introduced and analyzed the concept of implicative filters in quasi-ordered residuated systems. </em></p> 2021-03-04T00:00:00+00:00 Copyright (c) 2021 Daniel Romano Regularity and normality in ideal bitopological spaces 2020-06-23T21:21:07+00:00 Néstor Raúl Pachón Rubiano <p><em>We introduce, and study, the regularity and normality in ideal bitopological spaces, absent subject in literature. Our definitions have the advantage of using only the open sets of the two underlying topologies. These new concepts represent generalizations of Kelly's concepts of pairwise regularity and pairwise normality. The extension of the T<sub>0</sub>, T<sub>1</sub> and T<sub>2</sub> axioms to these spaces is due to Caldas et al.</em></p> 2021-03-04T00:00:00+00:00 Copyright (c) 2021 Néstor Raúl Pachón Rubiano A system of nonlinear fractional BVPs with ϕ-Laplacian operators and nonlocal conditions 2020-04-23T16:06:40+00:00 Bahia Temar Ouiza Saifi Smail Djebali <p><em>This work investigates the existence of multiple positive solutions for a system of two nonlinear higher-order fractional differential equations with ϕ-Laplacian operators and nonlocal conditions. A degenerate nonlinearity which obeys some general growth conditions is considered. The singularities are dealt with by approximating the fixed point operator. New existence results are presented by using the fixed point index theory. Examples of applications illustrate the theoretical results.</em></p> 2021-03-04T00:00:00+00:00 Copyright (c) 2021 Bahia Temar, Ouiza Saifi, Smail Djebali Some integral inequalities for approximately h-convex functions and their applications 2020-06-22T14:12:40+00:00 Artion Kashuri Muhammad Raees Matloob Anwar <p><em>In this paper, by applying the new and improved form of Hölder’s integral inequality called Hölder—Íşcan integral inequality three inequalities of Hermite—Hadamard and Hadamard integral type for (h, d)—convex functions have been established. Various special cases including classes for instance, h—convex, s—convex function of Breckner and Godunova—Levin—Dragomir and strong versions of the aforementioned types of convex functions have been identified. Some applications to error estimations of presented results have been analyzed. At the end, a briefly conclusion is given. </em></p> 2021-03-04T00:00:00+00:00 Copyright (c) 2021 Artion Kashuri, Muhammad Raees, Matloob Anwar Oscillation results for a certain class of fourth-order nonlinear delay differential equations 2020-05-22T13:39:10+00:00 Osama Moaaz Clemente Cesarano <p><em>In this work, we study the oscillation of the fourth order neutral differential equations with delay argument. By means of generalized Riccati transformation technique, we obtain new oscillation criteria for oscillation of this equation. An example is given to clarify the main results in this paper. </em></p> 2021-03-15T00:00:00+00:00 Copyright (c) 2021 Osama Moaaz, Clemente Cesarano Strong convergence theorem for family of minimization and monotone inclusion problems in Hadamard spaces 2020-05-24T22:59:47+00:00 Chinedu Izuchukwu Godwin C. Ugwunnadi Oluwatosin Temitope Mewomo <p><em>In this paper, we introduce a modified Ishikawa-type proximal point algorithm for approximating a common solution of minimization problem, monotone inclusion problem and fixed point problem. We obtain a strong convergence of the proposed algorithm to a common solution of finite family of minimization problem, finite family of monotone inclusion problem and fixed point problem for asymptotically demicontractive mapping in Hadamard spaces. Numerical example is given to illustrate the applicability of our main result. Our results complement and extend some recent results in literature.</em></p> 2021-03-15T00:00:00+00:00 Copyright (c) 2021 Dr. Chinedu Izuchukwu, Dr. Godwin C. Ugwunnadi, Prof. Oluwatosin T. Mewomo The forcing total monophonic number of a graph 2020-04-03T21:44:40+00:00 A. P. Santhakumaran P. Titus K. Ganesamoorthy M. Murugan <p><em>For a connected graph G = (V, E) of order at least two, a subset T of a minimum total monophonic set S of G is a forcing total monophonic subset for S if S is the unique minimum total monophonic set containing T . A forcing total monophonic subset for S of minimum cardinality is a minimum forcing total monophonic subset of S. The forcing total monophonic number f<sub>tm</sub>(S) in G is the cardinality of a minimum forcing total monophonic subset of S. The forcing total monophonic number of G is f<sub>tm</sub>(G) = min{f<sub>tm</sub>(S)}, where the minimum is taken over all minimum total monophonic sets S in G. We determine bounds for it and find the forcing total monophonic number of certain classes of graphs. It is shown that for every pair a, b of positive integers with 0 ≤ a &lt; b and b ≥ a+4, there exists a connected graph G such that f<sub>tm</sub>(G) = a and m<sub>t</sub>(G) = b.</em></p> 2021-03-15T00:00:00+00:00 Copyright (c) 2021 A. P. Santhakumaran, P. Titus, K. Ganesamoorthy, M. Murugan Applications of measure of noncompactness for the solvability of an infinite system of second order differential equations in some integrated sequence spaces 2020-04-28T17:15:43+00:00 Rituparna Das Niraj Sapkota <p><em>The aim of this paper is to study the infinite system of second order differential equations along with the given boundary conditions for its solvability in some integrated sequence spaces. The result is achieved with the analytical tool namely the measure of noncompactness along with the idea of Meir-Keeler condensing operator and provides the realization of the sufficient conditions for the existence results in these Banach Sequence spaces. We also illustrate the results with examples. </em></p> 2021-03-18T00:00:00+00:00 Copyright (c) 2021 Rituparna Das, Niraj Sapkota