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 27.05.2017
Creative Mathematics
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 Print Edition: ISSN 1584 - 286X Online Edition: ISSN 1843 - 441X Creative Math. and Inf. is a category B+ journal in the CNCSIS classification Indexed by: Mathematical Reviews Zentralblatt MATH Current rejection rate: 37.5 % RSS

Vol. 25 (2016), No. 1, 15 January 2016
 The $\Re_a$ operator in ideal topological spaces Author: Wadei Faris Al-Omeri, Mohd. Salmi Md. Noorani, T. Noiri and A. Al-Omari Abstract: Given a topological space $(X,\tau)$ an ideal $\mathcal{I}$ on $X$ and $A \subseteq X$, the concept of $a$-local function is defined as follows $A^{a^\ast}(\mathcal{I},\tau)=\{x \!\in\! X\!: U \!\cap A \notin \mathcal{I}, \,\text{for every}\,\, U \in \tau^{a}(x)\}$. In this paper a new type of space has been introduced with the help of $a$-open sets and the ideal topological space called \textbf{$a$}-ideal space. We introduce an operator $\Re_a : \wp(X)\rightarrow \tau$, for every $A \in \wp(X)$, and we use it to define some interesting generalized $a$-open sets and study their properties. PDF | No. of downloads: 94 Full access PDF | On $H_{3}(1)$ Hankel determinant for concave univalent functions Author: È˜ahsene AltÄ±nkaya and Sibel YalÃ§Ä±n Abstract: In this paper we study the class $C_{0}(\alpha )\left( \alpha \in (1,2]\right)$ - the class of the so-called concave univalent functions. The main aim is to obtain an upper bound to the third Hankel determinant for concave univalent functions. PDF | No. of downloads: 79 Full access PDF | A note on Baskakov operators based on a function $\vartheta$ Author: Didem AydÄ±n ArÄ±, Ali Aral and Daniel CÃ¡rdenas-Morales Abstract: In this paper, we consider a modification of the classical Baskakov operators based on a function $\vartheta$. Basic qualitative and quantitative Korovkin results are stated in weighted spaces. We prove a quantitative Voronovskaya-type theorem and present some results on the monotonic convergence of the sequence. Finally, we show a shape preserving property and further direct convergence theorems. Weighted modulus of continuity of first order and the notion of $\vartheta$-convexity are used throughout the paper. PDF | No. of downloads: 67 Full access PDF | On a notion of rapidity of convergence used in the study of fixed point iterative methods Author: Vasile Berinde Abstract: There exist many papers written in the last 50 years or so which are using a concept of rapidity of convergence for two comparable sequences. It appears that the original source of this notion is not known to most of the authors of those papers, since for this notion they are refereeing to different sources or simply do not refer to any other publication like this notion would be "folklore" or even like they would be the ones who introduced for the first time such a notion. Starting from this fact, the aim of the present note is to try to find out who was the true author of that notion of rapidity of convergence and, secondly, to illustrate how it is used in the particular case of the study of fixed point iterative methods. PDF | No. of downloads: 71 Full access PDF | Some new types of decomposition of continuity II Author: Carlos Carpintero, Jhon Moreno and Ennis Rosas Abstract: In this paper we extended (or generalized) the notions studied in [Carpintero, C. Moreno, J. and Rosas, E., Some New type of decomposition of continuity, submitted]. Using the notion of $\mu$-regular open set and $\mu$-semi regular open set, we introduce the concept of locally $\mu$-regular semi closed sets and locally $\mu$-semi regular semi closed sets and give a new theory of decomposition of continuity and some weak forms of continuity are studied. Also we improve some recent results due by [Roy, B. and Sen, R., On decomposition of weak continuity, Creat. Math. Inform, 24 (2015), No. 1-2, 83--88]. PDF | No. of downloads: 67 Full access PDF | Generalized connectedness and separation axioms of Minkowski space Author: Soley Ersoy and Merve Bilgin Abstract: In this study, we investigate the generalized connectedness of Minkowski space endowed with $s-$topology and obtain that $M^S$ is $\alpha-$connected but not semi, $\beta$ and $b-$connected. Moreover, we study separation axioms in Minkowski space and show that $M^S$ is $\alpha$, semi, $b$, $\beta$ and pre$-T_{i}$ $(i=0,1/2,1,2,5/2)$ space. PDF | No. of downloads: 75 Full access PDF | A comparative study on existing software quality models Author: Mara Diana Hajdu Macelaru Abstract: A comparison between main software quality models is done in this article. We analize the five quality models, we point out the good / bad issues in each model and we compare them based on the attributes/ characteristics, based on number of attributes as well as we define an algorithm to perform a comparison based on the importance of attributes in each model. PDF | No. of downloads: Full access PDF | Solutions of a system of integral equations with deviating argument Author: Monica Lauran Abstract: In this paper we establish two existence and uniqueness results for the solutions of a system of integral equations with deviating argument of the form $y_{1}(x)=f_{1}(x)+\int\limits_{a}^{b}K_{1}(x,y_1(y_1(s)),y_2(y_1(s)))ds.$ The solutions are searched in the set $C_{L}([a,b];[a,b]^2)$ and the main tool used in our study is the Perov's fixed point theorem. PDF | No. of downloads: Full access PDF | Remark on upper bounds of RandiÄ‡ index of a graph Author: I. Z. MilovanoviÄ‡, P. M. Bekakos, M. P. Bekakos and E. I. MilovanoviÄ‡ Abstract: Let $G=(V,E)$ be an undirected simple graph of order $n$ with $m$ edges without isolated vertices. Further, let $d_1\ge d_2\ge \cdots \ge d_n$ be vertex degree sequence of $G$. General RandiÄ‡ index of graph $G=(V,E)$ is defined by $\displaystyle R_{\alpha}=\sum_{(i,j)\in E}(d_id_j)^{\alpha}$, where $\alpha \in \mathbb{R} -\{0\}$. We consider the case when $\alpha =-1$ and obtain upper bound for $R_{-1}$. PDF | No. of downloads: 58 Full access PDF | Integral inequalities concerning polynomials with polar derivatives Author: Abdullah Mir and Shahista Bashir Abstract: Let $P(z)$ be a polynomial of degree $n$ and for any complex number $\alpha$, let $$D_\alpha P(z)=nP(z)+(\alpha-z)P^{\prime}(z)$$ denote the polar derivative of $P(z)$ with respect to a complex number $\alpha$. In this paper, we present an integral inequality for the polar derivative of a polynomial $P(z)$. Our result includes as special cases several interesting generalizations of some Zygmund type inequalities for polynomials. PDF | No. of downloads: 63 Full access PDF | Strong convergence results for nonlinear mappings in real Banach spaces Author: Adesanmi Alao Mogbademu Abstract: Let $X$ be a real Banach space, $K$ be a nonempty closed convex subset of $X$, $T: K \rightarrow K$ be a nearly uniformly $L$-Lipschitzian mapping with sequence $\{a_n\}.$ Let ${k_n}\subset [1,\infty)$ and $\epsilon_n$ be sequences with $\lim_{n\rightarrow\infty} k_n=1, \hspace{.05in}\lim_{n\rightarrow\infty} \epsilon_n=0$ and $F(T)=\{\rho\in K: T\rho=\rho\}\neq \emptyset.$ Let $\{\alpha_n\}_{n\geq 0}$ be real sequence in $[0,1]$ satisfying the following conditions: (i)$\sum_{n\geq 0}\alpha_n=\infty$ (ii) $\lim_{n\rightarrow\infty}\alpha_n=0$. For arbitrary $x_0\in K$, let $\{x_n\}_{n\geq 0}$ be iteratively defined by $x_{n+1}= (1-\alpha_n)x_n + \alpha_nT^nx_n,\hspace{.1in}n\geq 0$. If there exists a strictly increasing function $\Phi:[0,\infty)\rightarrow [0,\infty)$ with $\Phi(0)= 0$ such that $\left \leq k_n \|x -\rho\|^2 - \Phi(\|x -\rho\|)+\epsilon_n$ for all $x\in K$, then, $\{x_n\}_{n\geq 0}$ converges strongly to $\rho\in F(T)$. It is also proved that the sequence of iteration $\{x_n\}$ defined by $$x_{n+1} =(1-b_n-d_n)x_n+b_nT^nx_n+d_nw_n, n\geq 0,$$ where $\{w_n\}_{n\geq 0}$ is a bounded sequence in K and $\{b_n\}_{n\geq 0},\hspace{0.02in}\{d_n\}_{n\geq 0}$ are sequences in [0,1] satisfying appropriate conditions, converges strongly to a fixed point of $T$. PDF | No. of downloads: 64 Full access PDF | Strong twins of ordinary star-like self-contained graphs Author: Mohammad Hadi Shekarriz and Madjid Mirzavaziri Abstract: A self-contained graph is an infinite graph which is isomorphic to one of its proper induced subgraphs. In this paper, ordinary star-like self-contained graphs are introduced and it is shown that every ordinary star-like self-contained graph has infinitely many strong twins or none. PDF | No. of downloads: 59 Full access PDF | Estimating a special difference of harmonic numbers Author: Alina SÃ®ntÄƒmÄƒrian Abstract: The aim of this paper is to investigate a special difference of harmonic numbers. We obtain some limits and inequalities involving harmonic numbers and in the last part of the paper some open problems for investigation are posed. PDF | No. of downloads: 61 Full access PDF | Algorithm for Hammerstein equations with monotone mappings in certain Banach spaces Author: T. M. M. SOW, C. Diop and N. Djitte Abstract: For $q>1$ and $p>1$, let $E$ be a 2-uniformly convex and $q$-uniformly smooth or $p$- uniformly convex and $2$-uniformly smooth real Banach space and $F :E\to E^*$, $K: E^*\to E$ be bounded and strongly monotone maps with $D(K)=R(F)=E^*$. We construct a coupled iterative process and prove its strong convergence to a solution of the Hammerstein equation $u+KFu=0$. Futhermore, our technique of proof is of independent of interest. PDF | No. of downloads: 60 Full access PDF | Approximating fixed points of demicontractive mappings by iterative methods defined as admissible perturbations Author: Cristina ÈšicalÄƒ Abstract: The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces. PDF | No. of downloads: 69 Full access PDF |

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