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 Independent form of (?, s)-continuous functions in topological spaces <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> Brij K. Tyagi Sumit Singh Manoj Bhardwaj Copyright (c) 2020 Brij K. Tyagi, Sumit Singh, Manoj Bhardwaj 2020-06-03 2020-06-03 39 3 495 515 10.22199/issn.0717-6279-2020-03-0031 Total graph of a commutative semiring with respect to singular ideal <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> Nabanita Goswami Helen K. Saikia Copyright (c) 2020 Nabanita Goswami, Helen K. Saikia 2020-06-03 2020-06-03 39 3 517 527 10.22199/issn.0717-6279-2020-03-0032 Existence of solution for some quasilinear parabolic systems with weight and weak monotonicity <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> Azroul Elhoussine Barbara Abdelkrim Rami El Houcine Copyright (c) 2020 Azroul Elhoussine, Barbara Abdelkrim, Rami El Houcine 2020-06-03 2020-06-03 39 3 529 557 10.22199/issn.0717-6279-2020-03-0033 Discussion on relation-theoretic for JS-quasi-contractions of uni/milti-dimensional mappings with transitivity <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> Kanokwan Sawangsup Wutiphol Sintunavarat Copyright (c) 2020 Kanokwan Sawangsup, Wutiphol Sintunavarat 2020-06-03 2020-06-03 39 3 559 580 10.22199/issn.0717-6279-2020-03-0034 On a new difference sequence space <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> P. Baliarsingh L. Nayak P. Beuria Copyright (c) 2020 P. Baliarsingh, L. Nayak, P. Beuria 2020-06-03 2020-06-03 39 3 581 589 10.22199/issn.0717-6279-2020-03-0035 Maps preserving the square zero of ?-Lie product of operators <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> Ali Taghavi Roja Hosseinzadeh Masoomeh Yousefi Copyright (c) 2020 Ali Taghavi, Roja Hosseinzadeh, Masoomeh Yousefi 2020-06-03 2020-06-03 39 3 591 597 10.22199/issn.0717-6279-2020-03-0036 Convergence analysis for combination of equilibrium problems and k-nonspreading set-valued mappings <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> Suhel Ahmad Khan Khan Kaleem Raza Kazmi Watcharaporn Cholamjiak Hemen Dutta Copyright (c) 2020 Suhel Ahmad Khan Khan, Kaleem Raza Kazmi, Watcharaporn Cholamjiak, Hemen Dutta 2020-06-03 2020-06-03 39 3 599 619 10.22199/issn.0717-6279-2020-03-0037 Multi-item multi-objective fixed charged solid transportation problem with type-2 fuzzy variables <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> Dhiman Dutta Mausumi Sen Biplab Singha Copyright (c) 2020 Dhiman Dutta, Mausumi Sen, Biplab Singha 2020-06-03 2020-06-03 39 3 621 637 10.22199/issn.0717-6279-2020-03-0038 Sharp inequality of three point Gauss-Legendre quadrature rule <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> Artion Kashuri Copyright (c) 2020 Artion Kashuri 2020-05-28 2020-05-28 39 3 639 649 10.22199/issn.0717-6279-2020-03-0039 Effectiveness of Cannon and composite set of polynomials of two complex variables in Faber regions <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> Jerome Ajayi Adepoju Adesanmi Alao Mogbademu Copyright (c) 2020 Jerome Ajayi Adepoju, Adesanmi Alao Mogbademu 2020-06-03 2020-06-03 39 3 651 662 10.22199/issn.0717-6279-2020-03-0040 Erdelyi-Kober fractional Integrals on Hardy space and BMO <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> Kwok-Pun Ho Copyright (c) 2020 Kwok-Pun Ho 2020-06-03 2020-06-03 39 3 663 677 10.22199/issn.0717-6279-2020-03-0041 Some bounds for relative autocommutativity degree <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> Rajat Kanti Nath Parama Dutta Copyright (c) 2020 Rajat Kanti Nath, Parama Dutta 2020-06-03 2020-06-03 39 3 679 691 10.22199/issn.0717-6279-2020-03-0042 The P-Hausdorff, P-regular and P-normal ideal spaces <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> Néstor Raúl Pachón Rubiano Copyright (c) 2020 Néstor Raúl Pachón Rubiano 2020-05-14 2020-05-14 39 3 693 710 10.22199/issn.0717-6279-2020-03-0043 A Chebyshev pseudo spectral method for solving fractional differential equations <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> AllahBakhsh Yazdani Cherati Morteza Mohammadnezhad Kiasari Copyright (c) 2020 AllahBakhsh Yazdani Cherati, Morteza Mohammadnezhad Kiasari 2020-06-03 2020-06-03 39 3 711 720 10.22199/issn.0717-6279-2020-03-0044 The diophantine problem for addition and divisibility for subrings of rational functions over finite fields <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> Leonidas Antonio Cerda-Romero Carlos Martínez-Ranero Copyright (c) 2020 Leonidas Antonio Cerda-Romero, Carlos Martínez-Ranero 2020-06-03 2020-06-03 39 3 721 735 10.22199/issn.0717-6279-2020-03-0045