Proyecciones (Antofagasta, On line) 2020-06-03T16:38:11+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> Independent form of (?, s)-continuous functions in topological spaces 2020-05-20T03:15:43+00:00 Brij K. Tyagi Sumit Singh Manoj Bhardwaj <p><em>We introduce a new class of almost contra-P<sub>?</sub>-continuous functions which is a subclass of the class of almost contra-precontinuous functions [8]. This class contains the classes of regular set connected functions, perfectly continuous functions and contra-P<sub>?</sub>-continuous functions. It is shown that almost contra-P<sub>?</sub>-continuity is independent to (?, s)-continuity [12] and contra-precontinuity [11]. Furthermore, we obtain basic properties and preservations theorems for almost contra-P<sub>?</sub>-continuity.</em></p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 Brij K. Tyagi, Sumit Singh, Manoj Bhardwaj Total graph of a commutative semiring with respect to singular ideal 2020-05-23T04:03:32+00:00 Nabanita Goswami Helen K. Saikia <p><em>Let S be a commutative semiring with unity. The singular ideal Z(S) of S is defined as Z(S) = {s ? S | sK = 0 for some essential ideal K of S}. In this paper, we introduce the notion of total graph of a commutative semiring with respect to the singular ideal. We define this graph as the undirected graph T(?(S)) with all elements of S as vertices and any two distinct vertices x and y are adjacent if and only if x + y ? Z(S). We discuss various characteristics of this total graph and also characterize some important properties of certain induced subgraphs of this total graph.</em></p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 Nabanita Goswami, Helen K. Saikia Existence of solution for some quasilinear parabolic systems with weight and weak monotonicity 2020-05-25T16:31:07+00:00 Azroul Elhoussine Barbara Abdelkrim Rami El Houcine <p><em>We prove the existence of weak solution u for the nonlinear parabolic systems:</em></p> <p><em>which is a Dirichlet Problem. In this system, v belongs to </em>, <em>f and g satisfy some standards continuity and growth conditions. We prove existence of a weak solution of different variants of this system under classical regularity for some</em> growth and coercivity for ? but with only very mild monotonicity assumptions.</p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 Azroul Elhoussine, Barbara Abdelkrim, Rami El Houcine Discussion on relation-theoretic for JS-quasi-contractions of uni/milti-dimensional mappings with transitivity 2020-05-26T18:17:20+00:00 Kanokwan Sawangsup Wutiphol Sintunavarat <p><em>We introduce the notion of a </em><em>JS<sub>R </sub>quasi</em><em>-contraction mapping, where R </em><em>is a binary relation on its domain. Also, we prove some fixed point results for such contractions in complete metric spaces endowed with a transitive relation. An example is given to substantiate our obtained theorems. In addition, we introduce a JS</em><em><sub>R</sub></em><em><sub>N</sub></em><em> -quasicontraction and also establish fixed point of N-order theorems for such contractions.</em></p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 Kanokwan Sawangsup, Wutiphol Sintunavarat On a new difference sequence space 2020-05-26T18:10:28+00:00 P. Baliarsingh L. Nayak P. Beuria <p><em>In the present note, we define a new difference sequence </em><em>Dx </em><em>=(</em><em>Dx</em><em>)</em><em><sub>n</sub></em> <em>with the help of difference operator </em><em>D </em><em>as</em></p> <p><strong><em>&nbsp;</em></strong></p> <p>Also, we discuss some interesting properties of the proposed difference operator <em>D.</em></p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 P. Baliarsingh, L. Nayak, P. Beuria Maps preserving the square zero of ?-Lie product of operators 2020-05-26T18:53:59+00:00 Ali Taghavi Roja Hosseinzadeh Masoomeh Yousefi <p>Let B(H) be the algebra of all bounded linear operators on an infinite dimensional Hilbert space ?. In this paper, we identify the form of the unital surjective additive map ? : B(H)? B(H)which preserves the square zero of ?-Lie product of operators for some scalar ? with ? ? 0, 1, ?1.</p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 Ali Taghavi, Roja Hosseinzadeh, Masoomeh Yousefi Convergence analysis for combination of equilibrium problems and k-nonspreading set-valued mappings 2020-05-27T16:41:46+00:00 Suhel Ahmad Khan Khan Kaleem Raza Kazmi Watcharaporn Cholamjiak Hemen Dutta <p>We find a common solution of generalized equilibrium problems and the set of fixed points of a k-nonspreading setvalued mapping by using shrinking projection hybrid method. Finally, we compare the shrinking solution set after randomization by giving numerical example which justifies our main result.</p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 Suhel Ahmad Khan Khan, Kaleem Raza Kazmi, Watcharaporn Cholamjiak, Hemen Dutta Multi-item multi-objective fixed charged solid transportation problem with type-2 fuzzy variables 2020-05-28T02:57:32+00:00 Dhiman Dutta Mausumi Sen Biplab Singha <p><em>A multi-item multi-objective fixed charged solid transportation problema with guidelines e.g. unit transportation penalty, amounts, requirements, and conveyances as type-2 triangular fuzzy variables with conditions on few items and conveyances is formulated here. A chance constrained programming model applying generalized credibility measure for the objective function as well as the constraints is formed with the critical value based reductions of corresponding type-2 fuzzy guidelines for this particular problem. The model is then converted into the equivalent crisp deterministic form. The optimal compromise solutions are obtained by fuzzy programming technique. An example is contributed to highlight the model and is then solved by applying Generalized Reduced Gradient (GRG) technique (applying LINGO 16). The sensitivity analysis of the model is also given to illustrate the model.</em></p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 Dhiman Dutta, Mausumi Sen, Biplab Singha Sharp inequality of three point Gauss-Legendre quadrature rule 2020-05-28T04:45:33+00:00 Artion Kashuri <p>An interesting identity for 3-point Gauss-Legendre quadrature rule using functions that are n-times differentiable. By applying the established identity, a sharp inequality which gives an error bound for 3-point Gauss-Legendre quadrature rule and some generalizations are derived. At the end, an application in numerical integration is given.</p> 2020-05-28T00:00:00+00:00 Copyright (c) 2020 Artion Kashuri Effectiveness of Cannon and composite set of polynomials of two complex variables in Faber regions 2020-05-28T02:54:02+00:00 Jerome Ajayi Adepoju Adesanmi Alao Mogbademu <p>Conditions are obtained for effectiveness of Cannon and Composite sets of polynomials of two complex variables in Faber regions. It generalizes to these regions the results of Nassif on composite sets in balls of centre origin whose constituents are also cannon sets.</p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 Jerome Ajayi Adepoju, Adesanmi Alao Mogbademu Erdelyi-Kober fractional Integrals on Hardy space and BMO 2020-02-26T01:54:25+00:00 Kwok-Pun Ho <p><em>The mapping properties of the multi. Erdélyi- Kober fractional integral operators on Hardy space and BMO. In particular, our main result gives the boundedness of the Erdélyi-Kober fractional integrals, the hypergeometric fractional integrals and the two-dimensional Weyl integrals on Hardy space and BMO.</em></p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 Kwok-Pun Ho Some bounds for relative autocommutativity degree 2020-04-22T03:48:51+00:00 Rajat Kanti Nath Parama Dutta <pre>We consider the probability that a randomly chosen element of a subgroup of a finite group $G$ is fixed by an automorphism of $G$. We obtain several bounds for this probability and characterize some finite groups with respect to this probability. </pre> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 Rajat Kanti Nath, Parama Dutta The P-Hausdorff, P-regular and P-normal ideal spaces 2020-05-28T05:01:36+00:00 Néstor Raúl Pachón Rubiano <p><em>We introduce and study new extensions of some separation axioms to ideal topological spaces, which we have called <strong>????</strong>-Hausdorff, <strong>????</strong>-regular and <strong>????</strong>-normal. These extensions are quite natural and represent a good improvement with respect to other extensions that have recently occurred, in which a level of separation that can be considered acceptable is not perceived.</em></p> <p> </p> 2020-05-14T00:00:00+00:00 Copyright (c) 2020 Néstor Raúl Pachón Rubiano A Chebyshev pseudo spectral method for solving fractional differential equations 2019-12-13T23:25:08+00:00 AllahBakhsh Yazdani Cherati Morteza Mohammadnezhad Kiasari <p><em><span class="fontstyle0">The Chebyshev pseudo-spectral method is generalized for solving fractional differential equations with initial conditions. For this purpose, an appropriate representation of the solution is presented and the Chebyshev pseudo-spectral differentiation matrix of fractional order is derived. Then, by using Chebyshev pseudo-spectral scheme, the problem is reduced to the solution of a system of algebraic equations.</span></em></p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 AllahBakhsh Yazdani Cherati, Morteza Mohammadnezhad Kiasari The diophantine problem for addition and divisibility for subrings of rational functions over finite fields 2019-10-04T23:00:30+00:00 Leonidas Antonio Cerda-Romero Carlos Martínez-Ranero <p><em>It is shown that the positive existential theory of the structure </em>?<sub>S</sub> = (S<sup>?1</sup>F[<em>t</em>];=,F, 0, 1,+, |,<em> f </em>? <em>tf), where f </em><em>?</em><em> tf is the multiplication by t map, S is non-empty a finite set of irreducible polynomials, and F is a finite field of odd characteristic, is undecidable</em>.</p> 2020-06-03T00:00:00+00:00 Copyright (c) 2020 Leonidas Antonio Cerda-Romero, Carlos Martínez-Ranero