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Print Edition: ISSN 1584 - 286X
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Contents (PDF)
Vol. 24 (2015), No. 1, 31 May 2015
Multivalued almost contractions in metric space endowed with a graph
Author: Ishak Altun / Ozlem Acar
Abstract: The main goal of this paper is to introduce a multivalued almost contraction on a metric space with a graph. In terms of this new contraction, we establish some fixed point results on graph.
No. of downloads: 194 Full access PDF |
On a functional equation arising in mathematical biology and theory of learning
Author: Vasile Berinde / Abdul Rahim Khan
Abstract: V. Istrățescu [Istrățescu, V. I., On a functional equation, J. Math. Anal. Appl., 56 (1976), No. 1, 133--136] used the Banach contraction mapping principle to establish an existence and approximation result for the solution of the functional equation $$ \varphi(x)=x \varphi((1-\alpha)x+\alpha)+(1-x)\varphi((1-\beta)x), \,x\in [0,1],\,(0<\alpha\leq \beta <1), $$ which is important for some mathematical models arising in biology and theory of learning. This equation has been studied by Lyubich and Shapiro [A. P. Lyubich, Yu. I. and Shapiro, A. P., On a functional equation (Russian), Teor. Funkts., Funkts. Anal. Prilozh. 17 (1973), 81--84] and subsequently, by Dmitriev and Shapiro [Dmitriev, A. A. and Shapiro, A. P., On a certain functional equation of the theory of learning (Russian), Usp. Mat. Nauk 37 (1982), No. 4 (226), 155--156]. The main aim of this note is to solve this functional equation with more general arguments for $\varphi$ on the right hand side, by using appropriate fixed point tools.
No. of downloads: 166 Full access PDF |
Convergence properties of Ibragimov-Gadjiev-Durrmeyer operators
Author: Emre Deniz / Ali Aral
Abstract: The purpose of the present paper is to study the local and global direct approximation properties of the Durrmeyer type generalization of Ibragimov Gadjiev operators defined in [Aral, A. and Acar, T., On Approximation Properties of Generalized Durrmeyer Operators, (submitted)]. The results obtained in this study consist of Korovkin type theorem which enables us to approximate a function uniformly by new Durrmeyer operators, and estimate for approximation error of the operators in terms of weighted modulus of continuity. These results are obtained for the functions which belong to weighted space with polynomial weighted norm by new operators which act on functions defined on the non compact interval $[0.\infty )$. We finally present a direct approximation result.
No. of downloads: 151 Full access PDF |
A survey on the stability of mean value points and functional equations involving some special functions
Author: Sorinel Dumitrescu / Mihai Moneaand Cristinel Mortici
Abstract: The aim of this work is to put together some of the recent and classical results in the theory of stability. In the first part, we recall the results regarding the intermediary points arising from various Mean Value Theorems, then we study the stability of some functional equations involving the gamma and beta functions.
No. of downloads: 159 Full access PDF |
Commuting Regularity degree of finite semigroups
Author: A. Firuzkuhy / H. Doostie
Abstract: A pair $(x,y)$ of elements $x$ and $y$ of a semigroup $S$ is said to be a commuting regular pair, if there exists an element $z\in S$ such that $xy=(yx)z(yx)$. In a finite semigroup $S$, the probability that the pair $(x,y)$ of elements of $S$ is commuting regular will be denoted by $dcr(S)$ and will be called the Commuting Regularity degree of $S$. Obviously if $S$ is a group, then $dcr(S)=1$. However for a semigroup $S$, getting an upper bound for $dcr(S)$ will be of interest to study and to identify the different types of non-commutative semigroups. In this paper, we calculate this probability for certain classes of finite semigroups. In this study we managed to present an interesting class of semigroups where the probability is $\frac{1}{2}$. This helps us to estimate a condition on non-commutative semigroups such that the commuting regularity of $(x,y)$ yields the commuting regularity of $(y,x)$.
No. of downloads: 131 Full access PDF |
Computing the Wiener index of graphs on triples
Author: M. Ghorbani
Abstract: Let $S$ be a set of size $n\geq 8$ and $V$ be the set of all subsets of $S$ of size $3$. Three types of intersection graphs $G_{i}(n),i=0,1,2$, can be defined with the vertex set $V$ whose Wiener indices will be calculated in this paper.
No. of downloads: 150 Full access PDF |
On some weak separation axioms
Author: Sabir Hussain
Abstract: We introduce and explore weak separation axioms namely $\gamma$-semi-$T_{i}$( for $i = 0, 1, 2$) spaces. We also define and discuss $\gamma$-semi-$D_{i}$( for $i = 0, 1, 2$) spaces and develop the relations between these spaces. Moreover, we initiate the concept of $\gamma$-S-continuous function and discuss the behavior of $\gamma$-semi-$D_{1}$ space under $\gamma$-S-continuous function.
No. of downloads: 153 Full access PDF |
Note on a Schurer-Stancu-type operator
Author: Adrian D. Indrea / Anamaria Indrea / Petru I. Braica
Abstract: The aim of this paper is to introduce a class of operators of Schurer-Stancu-type with the property that the test functions $e_0$ and $e_1$ are reproduced. Also, in our approach, a theorem of error approximation and a Voronovskaja-type theorem for this operators are obtained. Finally, we study the convergence of the iterates for our new class of operators.
No. of downloads: 146 Full access PDF |
Coefficient inequality for transforms of starlike and convex functions
Author: D. Vamshee Krishna / B. Venkateswarlu / T. RamReddy
Abstract: The objective of this paper is to obtain an upper bound for the second Hankel functional associated with the $k^{th}$ root transform $\left[ f(z ^k ) \right] ^{\frac{1}{k}}$ of normalized analytic function $f(z)$ belonging to starlike and convex functions, defined on the open unit disc in the complex plane, using Toeplitz determinants.
No. of downloads: 138 Full access PDF |
Common fixed point and best approximation results for subcompatible mappings in hyperbolic ordered metric spaces
Author: Savita Rathee / Reetu
Abstract: In the present paper we establish a common fixed point theorem and apply it to find new best approximation results for ordered subcompatible mappings in the hyperbolic ordered metric space. Our results unify, generalize and complement various known results.
No. of downloads: 141 Full access PDF |
On decomposition of weak continuity
Author: Bishwambhar Roy / Ritu Sen
Abstract: In this paper, the notions of locally $\mu$-regular closed sets, $\widehat{\mu}$-$t$-sets, $\widehat{\mu}$-$B$-sets have been introduced. Using these concepts, the decomposition of some weak forms of continuity have been studied.
No. of downloads: 155 Full access PDF |
$k$-Combinations of an unlabelled graph
Author: M. R. Ebrahimi Vishki / K. Mirzavaziri / M. Mirzavaziri
Abstract: In this paper we extend the notion of the binomial coefficient $n\choose k$ into a new notion $[G]\choose k$, where $[G]$ is an unlabelled graph with $n$ vertices and $0\leqslant k\leqslant n$. We call $[G]\choose k$ as the graph binomial coefficient and a version of the graph binomial expansion is also studied. As an application of this notion, we enumerate the number of ways to color vertices of a path and beads of a necklace.
No. of downloads: 127 Full access PDF |
A Banach algebra which is generated by idempotents
Author: A. Zivari-Kazempour
Abstract: In this paper we show that the Banach algebra $C_0(X)$, where $ X$ is a locally compact Hausdorff space, is generated by idempotents if and only if $X$ is totally disconnected.
No. of downloads: 142 Full access PDF |

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