Proyecciones. Journal of Mathematics <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 4 números al año.</p> Universidad Católica del Norte es-ES Proyecciones. Journal of Mathematics 0716-0917 Super vertex mean labeling of cycles through different ways <p>A super vertex mean labeling f of a (p, q) - graph G = (V,E) is defined as an injection from E to the set {1, 2, 3, ··· , p + q} that induces for each vertex v the label defined by the rule f<span style="font-size: 11.6667px;"><sup>v</sup></span>(v) = Round&nbsp;<img src=""> , where E<sub>v</sub> denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1, 2, 3, ··· , p + q}. In this paper, we investigate the super vertex mean labeling behavior of cycles by giving various ways by which they can be labeled.</p> A. Lourdusamy Sherry George ##submission.copyrightStatement## 2018-06-05 2018-06-05 37 2 181 198 On estimates for the generalized Fourier-Bessel transform <p><img src="/public/site/images/admin/a13_199_211.png"></p> A. Akhlidj R. Daher M. El Hamma ##submission.copyrightStatement## 2018-06-05 2018-06-05 37 2 199 211 Saturations of submodules with respect to subsets of a ring <p>Let R be a commutative ring with identity and M a unital R-module.</p> Javad Bagheri Harehdashti Hosein Fazaeli Moghimi ##submission.copyrightStatement## 2018-06-06 2018-06-06 37 2 213 221 Generalised Closed Sets in Multiset Topological Space <p>In this article, we introduce the notion of generalized closed sets and generalized open sets in multiset topological spaces. We investigate their different properties. We have introduced the notion of some separation axioms and discussed some examples.</p> Karishma Shravan Binod Chandra Tripathy ##submission.copyrightStatement## 2018-06-07 2018-06-07 37 2 223 237 A new family of chromatically unique 6-bridge graph <p>For a graph G, let P(G, λ) denote the chromatic polynomial of&nbsp;G. Two graphs G and H are chromatically equivalent (or simply&nbsp;χ−equivalent), denoted by G ∼ H, if P(G, λ) = P(H, λ). A graph&nbsp;G is chromatically unique (or simply χ−unique) if for any graph H&nbsp;such as H ∼ G, we have H ∼&nbsp;= G, i.e, H is isomorphic to G. In this&nbsp;paper, the chromatic uniqueness of a new family of 6-bridge graph<br>θ(a, a, b, b, b, c) where 2 ≤ a ≤ b ≤ c, is investigated.</p> N. S. A. Karim R. Hasni ##submission.copyrightStatement## 2018-06-07 2018-06-07 37 2 239 263 A general method for to decompose modular multiplicative inverse operators over Group of units <p>In this article, the notion of modular multiplicative inverse operator (MMIO)</p> Luis A. Cortés Vega ##submission.copyrightStatement## 2018-06-07 2018-06-07 37 2 265 293 Upper double monophonic number of a graph <p>A set S of a connected graph G of order n is called a double monophonic set of G if for every pair of vertices x, y in G there exist vertices u, v in S such that x, y lie on a u − v monophonic path. The double monophonic number dm(G) of G is the minimum cardinality of a double monophonic set. A double monophonic set S in a connected graph G is called a minimal double monophonic set if no proper subset of S is a double monophonic set of G. The upper double monophonic number of G is the maximum cardinality of a minimal double monophonic set of G, and is denoted by dm⁺(G). Some general properties satisfied by upper double monophonic sets are discussed. It is proved&nbsp; that for a connected graph G of order n, dm(G) = n if and only if&nbsp;dm⁺(G) = n. It is also proved that dm(G) = n − 1 if and only if dm⁺ (G) = n − 1 for a non-complete graph G of order n with a full degree vertex. For any positive integers 2 ≤ a ≤ b, there exists a connected graph G with dm(G) = a and dm⁺(G) = b.</p> A. P. Santhakumaran T. Venkata Raghu ##submission.copyrightStatement## 2018-06-06 2018-06-06 37 2 295 304 Bound on H3(1) Hankel determinant for pre-starlike functions of order α <p>The objective of this paper is to obtain best possible upper bound to the third Hankel determinant for the pre-starlike functions of order α (0 ≤ α &lt; 1), using Toeplitz determinants.</p> D. Vamshee Krishna D. Shalini ##submission.copyrightStatement## 2018-06-06 2018-06-06 37 2 305 315 Solutions and stability of a variant of Wilson’s functional equation <p>In this paper we will investigate the complex-valued solutions and stability of the generalized variant of Wilson’s functional equation</p> <p>(E) : f(xy) + χ(y)f(σ(y)x) = 2f(x)g(y), x, y ∈ G,</p> <p><br> where G is a group, σ is an involutive morphism of G and χ is a character of G. (a) We solve (E) when σ is an involutive automorphism, and we obtain some properties about solutions of (E) when σ is an involutive anti-automorphism. (b) We obtain the Hyers Ulam stability of equation (E). As an application, we prove the superstability of the functional equation f(xy) + χ(y)f(σ(y)x) = 2f(x)f(y), x, y ∈ G.</p> Elhoucien Elqorachi Ahmed Redouani ##submission.copyrightStatement## 2018-06-06 2018-06-06 37 2 317 344 Riemann-Liouville fractional trapezium-like inequalities via generalized (m, h₁, h₂)-preinvexity <p>In this paper, we derive a fractional integral identity concerning three times differentiable generalized preinvex mappings defined on minvex set. By using of this identity, we obtain new estimates on generalization of trapezium-like inequalities for functions whose third order derivatives are generalized (m, h₁, h₂)-preinvex via Riemann-Liouville fractional integrals. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.</p> Piao Guo Zhengzheng Huang Tingsong Du ##submission.copyrightStatement## 2018-06-06 2018-06-06 37 2 345 378 On velocity bimagnetic biharmonic particles with energy on Heisenberg space <p>In this work, we consider velocity bimagnetic biharmonic particle on 3D Heisenberg space in the magnetic field B and we give the concept of energy. Moreover, we characterize energy conditions of velocity bimagnetic biharmonic particles with Frenet vector field. Therefore, we obtain energy results for bimagnetic particles by Frenet fields in the Heisenberg space.</p> Talat Körpinar ##submission.copyrightStatement## 2018-06-06 2018-06-06 37 2 379 387 Fuzzy normed linear sequence space bvFp (X) <p>In this article we introduce the notion of class of sequences&nbsp;bv<sup>F</sup><sub>p</sub> (X),1 ≤ p &lt; ∞ with the concept of fuzzy norm. We study some of&nbsp;its properties such as completeness, solidness, symmeticity and convergence free. Also, we establish some inclusion results.</p> Paritosh Chandra Das ##submission.copyrightStatement## 2018-06-06 2018-06-06 37 2 389 403