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.
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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.
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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.
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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.
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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].
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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.
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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.
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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.
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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 $R_{-1}$.
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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.
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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 $T$.
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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.
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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.
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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.
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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.
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