# Volume 27 (2019): Edition 1 (June 2019)

Détails du magazine
Format
Magazine
eISSN
1584-3289
Première publication
30 Jul 2019
Période de publication
2 fois par an
Langues
Anglais

9 Articles
Accès libre

#### On Neighbor chromatic number of grid and torus graphs

Publié en ligne: 21 Dec 2019
Pages: 3 - 15

#### Résumé

A set SV is a neighborhood set of a graph G = (V, E), if G = ∪v∈SN[v] 〉, where 〈 N[v] 〉 is the subgraph of a graph G induced by v and all vertices adjacent to v. A neighborhood set S is said to be a neighbor coloring set if it contains at least one vertex from each color class of a graph G, where color class of a colored graph is the set of vertices having one particular color. The neighbor chromatic number χn (G) is the minimum cardinality of a neighbor coloring set of a graph G. In this article, some results on neighbor chromatic number of Cartesian products of two paths (grid graph) and cycles (torus graphs) are explored.

#### Mots clés

• Neighborhood number
• chromatic number
• neighbor chromatic number
• grid graph
• torus graph

• 05C15
• 05C70
Accès libre

#### Arens simultaneously factorization

Publié en ligne: 21 Dec 2019
Pages: 17 - 27

#### Résumé

Let X be a Banach bimodule over a Banach algebra 𝒜. We shall seek conditions under which (1) X and its dual factorize on the same side or (2) X factors on the left (or right) if and only if its second conjugate space has a left (or right) unit.

#### Mots clés

• Banach algebra
• Banach bimodule
• mixed units
• arens product

#### MSC 2010

• Primary 46L06
• Secondary 46L07
Accès libre

#### Properties of the intermediate point from a mean value theorem of the integral calculus - II

Publié en ligne: 21 Dec 2019
Pages: 29 - 36

#### Résumé

In this paper we consider two continuous functions f, g : [a, b] → ℝ and we study for these ones, under which circumstances the intermediate point function is four order di erentiable at the point x = a and we calculate its derivative.

#### Mots clés

• intermediate point
• mean-value theorem

• 26A24
• 11H60
Accès libre

#### Notes on certain p-valent functions

Publié en ligne: 21 Dec 2019
Pages: 37 - 43

#### Résumé

Let Ap be the class of functions f(z) which are analytic in the open unit disk U. Applying some subordinations for functions, some interesting properties for f(z) ∈Ap are showed. Our results are generalizations for results given before.

#### Mots clés

• analytic functions
• -valent functions
• univalent functions
• subordination

• 30C45
• 30C80
Accès libre

#### Forgotten topological index and reduced Zagreb index of four new operations of graphs

Publié en ligne: 21 Dec 2019
Pages: 45 - 56

#### Résumé

Indulal and Balakrishnan (2016) have put forward the Indu-Bala product and based on this product four new operations are defined by the authors of this manuscript in the paper “Four new operations of graphs based on Indu-Bala product and the Zagreb indices”. In this paper we establish explicit formulas of the forgotten topological index and reduced second Zagreb index in connection with these new operations of graphs.

#### Mots clés

• forgotten topological index
• reduced Zagreb index
• operations of graphs

• 05C76
• 05C07
Accès libre

#### Consensus of classical and fractional inequalities having congruity on time scale calculus

Publié en ligne: 21 Dec 2019
Pages: 57 - 69

#### Résumé

In this paper, we find accordance of some classical inequalities and fractional dynamic inequalities. We find inequalities such as Radon’s inequality, Bergström’s inequality, Rogers-Hölder’s inequality, Cauchy-Schwarz’s inequality, the weighted power mean inequality and Schlömilch’s inequality in generalized and extended form by using the Riemann-Liouville fractional integrals on time scales.

#### Mots clés

• Time scales
• Riemann-Liouville fractional integrals

• 26D15
• 26D20
• 26A33
• 39A12
Accès libre

#### A study of fractional integro-differential equations via Hilfer-Hadamard fractional derivative

Publié en ligne: 21 Dec 2019
Pages: 71 - 84

#### Résumé

In this paper, we investigate the existence of solution of integro-differential equations (IDEs) with Hilfer-Hadamard fractional derivative. The main results are obtained by using Schaefer’s fixed point theorem. Some Ulam stability results are presented.

#### Mots clés

• Fractional integro-differential equations
• Hilfer fractional derivative
• Solution
• Ulam-Hyers stablity

• 26A33
• 60H10
• 34K30
• 34K40
Accès libre

#### Some strong and weak form of z-continuity via Cl*

Publié en ligne: 21 Dec 2019
Pages: 85 - 101

#### Résumé

This paper mainly dedicated on overview of zero sets in Ideal topological spaces. We also introduce a new class of functions which generalizes the class of continuous functions and investigate its position in the hierarchy of continuous functions on Ideal topological spaces. Moreover, these new sets (zero*-ℐ-set) which is a pragmatic approach to characterize completely Hausdorff spaces.

#### Mots clés

• Ideal
• zero sets
• z-open
• z-continuous
• Completely Hausdor

• 54C05
• 54C08
• 54C10
Accès libre

#### Book Review: Recent Advances in Constructive Approximation Theory By: V. Gupta, T.M. Rassias, P.N. Agrawal, A.M. Acu Springer Optim. Appl. 138, Springer, Cham, 2018, DOI 10.1007/978-3-319-92165-5

Publié en ligne: 21 Dec 2019
Pages: 103 - 103