<abstract xmlns="http://www.w3.org/1999/xhtml">A set <italic>S</italic> ⊆ <italic>V</italic> is a neighborhood set of a graph <italic>G</italic> = (<italic>V, E</italic>), if <italic>G</italic> = ∪<italic>v∈S</italic> 〈 <italic>N</italic>[<italic>v</italic>] 〉, where 〈 <italic>N</italic>[<italic>v</italic>] 〉 is the subgraph of a graph <italic>G</italic> induced by <italic>v</italic> and all vertices adjacent to <italic>v</italic>. A neighborhood set <italic>S</italic> is said to be a neighbor coloring set if it contains at least one vertex from each color class of a graph <italic>G</italic>, where color class of a colored graph is the set of vertices having one particular color. The neighbor chromatic number χ<italic>n</italic> (<italic>G</italic>) is the minimum cardinality of a neighbor coloring set of a graph <italic>G</italic>. In this article, some results on neighbor chromatic number of Cartesian products of two paths (grid graph) and cycles (torus graphs) are explored.</abstract>

On Neighbor chromatic number of grid and torus graphs

<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>X</italic> be a Banach bimodule over a Banach algebra 𝒜. We shall seek conditions under which (1) <italic>X</italic> and its dual factorize on the same side or (2) <italic>X</italic> factors on the left (or right) if and only if its second conjugate space has a left (or right) unit.</abstract>

Arens simultaneously factorization

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we consider two continuous functions <italic>f, g</italic> : [<italic>a, b</italic>] → ℝ and we study for these ones, under which circumstances the intermediate point function is four order di erentiable at the point <italic>x</italic> = <italic>a</italic> and we calculate its derivative.</abstract>

Faculty of Mathematics and Computer Science, Department of Mathematics

Faculty of Science Department of Mathematics and Computer Science

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

<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>Ap</italic> be the class of functions <italic>f</italic>(<italic>z</italic>) which are analytic in the open unit disk <italic>U</italic>. Applying some subordinations for functions, some interesting properties for <italic>f</italic>(<italic>z</italic>) ∈<italic>Ap</italic> are showed. Our results are generalizations for results given before.</abstract>

Faculty of Science, Department of Mathematics and Informatics

1 Decembrie 1918 University of Alba Iulia

Notes on certain p-valent functions

<abstract xmlns="http://www.w3.org/1999/xhtml">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.</abstract>

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

<abstract xmlns="http://www.w3.org/1999/xhtml">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.</abstract>

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

<abstract xmlns="http://www.w3.org/1999/xhtml">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.</abstract>

Department of Mathematics, Faculty of Science

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

<abstract xmlns="http://www.w3.org/1999/xhtml">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 <italic>Hausdorff</italic> spaces.</abstract>

Some strong and weak form of z-continuity via <italic>Cl</italic>*

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

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General Mathematics

 Publishing House and Owner: Lucian Blaga University of Sibiu, Romania   General Mathematics publishes high quality papers on pure and applied mathematics. To be published in this journal, a paper must contain new ideas and be of interest to a wide range of readers. Survey papers are also welcome.The journal appears in 2 numbers per year and has been published since 1993.It is edited by the Department of Mathematics and Informatics of the “Lucian Blaga” University of Sibiu.  The purpose of General Mathematics is to provide an outlet for high quality original research in all areas of analysis or that having applications in economics, engineering, the life sciences, physics and statistical decision theory.  Coverage touches on a wide variety of topics, including:   Functional analysis and operator theory  Real and harmonic analysis　  Complex analysis　  Numerical analysis　  Applied mathematics　  Partial differential equations　  Dynamical systems　  Control and Optimization　  Probability　  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. 