23.04.2017   




Print Edition: ISSN 1584 - 2851
Online Edition: ISSN 1843 - 4401


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Vol. 33 (2017), No. 1, 15 December 2016
 
Stability in non-autonomous periodic systems with grazing stationary impacts
Author: Marat Akhmet and Aysegul Kivilcim
Abstract: This paper examines impulsive non-autonomous periodic systems whose surfaces of discontinuity and impact functions are not depending on the time variable. The $W-$map which alters the system with variable moments of impulses to that with fixed moments and facilitates the investigations, is presented. A particular linearizion system with two compartments is utilized to analyze stability of a grazing periodic solution. A significant way to keep down a singularity in linearizion is demonstrated. A concise review on sufficient conditions for the linearizion and stability is presented. An example is given to actualize the theoretical results.
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Iterative methods for generalized split feasibility problems in Banach spaces
Author: Qamrul Hasan Ansari and Aisha Rehan
Abstract: Inspired by the recent work of Takahashi et al. [W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, Set-Valued Var. Anal., 23 (2015), 205--221], in this paper, we study generalized split feasibility problems (GSFPs) in the setting of Banach spaces. We propose iterative algorithms to compute the approximate solutions of such problems. The weak convergence of the sequence generated by the proposed algorithms is studied. As applications, we derive some algorithms and convergence results for some problems from nonlinear analysis, namely, split feasibility problems, equilibrium problems, etc. Our results generalize several known results in the literature including the results of Takahashi et al. W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, Set-Valued Var. Anal., 23 (2015), 205--221.
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Extending the applicability of Newton's method using Wang's-- Smale's $\alpha$--theory
Author: Ioannis K. Argyros and Santhosh George
Abstract: We improve semilocal convergence results for Newton's method by defining a more precise domain where the Newton iterate lies than in earlier studies using the Smale's $\alpha$-- theory. These improvements are obtained under the same computational cost. Numerical examples are also presented in this study to show that the earlier results cannot apply but the new results can apply to solve equations.
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On the Voronovskaja-type formula for the Bleimann, Butzer and Hahn bivariate operators
Author: Dan Bărbosu and Dan Miclăuș
Abstract: In this paper we present two new alternative ways for the proof of Voronovskaja-type formula of the Bleimann, Butzer and Hahn bivariate operators, using the close connection between the recalled operators and Bernstein bivariate operators, respectively Stancu bivariate operators.
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On an isomorphism lying behind the class number formula
Author: Vlad Crișan
Abstract: Let $p$ be an odd prime such that the Greenberg conjecture holds for the maximal real cyclotomic subfield $\mathbb{K}_1$ of $\mathbb{Q}[ \zeta_p ]$. Let $A_n = (\mathcal{C}(\mathbb{K}_n))_p$ be the $p$-part of the class group of $\mathbb{K}_n$, the $n$-th field in the cyclotomic tower, and let $\underline{E}_n$, $\underline{C}_n$ be the global and cyclotomic units of $\mathbb{K}_n$, respectively. We prove that under this premise, there is some $n_0$ such that for all $m \geq n_0$, the class number formula $\left|\left(\underline{E}_m/\underline{C}_m\right)_p\right|=|A_m|$ hides in fact an isomorphism of $\Lambda[\hbox{Gal}(\mathbb{K}_1/\mathbb{Q})]$-modules.
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Quantitative estimates in uniform and pointwise approximation by Bernstein-Durrmeyer-Choquet operators
Author: Sorin G. Gal and Sorin Trifa
Abstract: For the qualitative results of uniform and pointwise approximation obtained in [Gal-Opris], we present here general quantitative estimates in terms of the modulus of continuity and of a $K$-functional, in approximation by the generalized multivariate Bernstein-Durrmeyer operator $M_{n, \Gamma_{n, x}}$, written in terms of Choquet integrals with respect to a family of monotone and submodular set functions, $\Gamma_{n, x}$, on the standard $d$-dimensional simplex. If $d=1$ and the Choquet integrals are taken with respect to some concrete possibility measures, the estimate in terms of the modulus of continuity is detailed. Examples improving the estimates given by the classical operators also are presented.
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New Suzuki-Berinde type fixed point results
Author: N. Hussain and J. Ahmad
Abstract: The aim of this article is to improve the results of Piri et al. [Fixed Point Theory and Applications 2014, 2014:210] by introducing new types of contractions say Suzuki-Berinde type $F$-contractions and Suzuki type rational $F$-contractions. We also establish a common fixed point theorem for a sequence of multivalued mappings. An example is also given to support our main results.
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Bezier variant of genuine-Durrmeyer type operators based on Polya distribution
Author: Trapti Neer, Ana Maria Acu and P. N. Agrawal
Abstract: In this paper we introduce the Bezier variant of genuine-Durrmeyer type operators having P\'{o}lya basis functions. We give a global approximation theorem in terms of second order modulus of continuity, a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem by using the Ditzian-Totik modulus of smoothness. The rate of convergence for functions whose derivatives are of bounded variation is obtained. Further, we show the rate of convergence of these operators to certain functions by illustrative graphics using the Maple algorithms.
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Hardy-Littlewood-Polya theorem of majorization in the framework of generalized convexity
Author: Constantin P. Niculescu and Ionel Rovența
Abstract: Based on a new concept of generalized relative convexity, a large extension of Hardy-Littlewood-Polya theorem of majorization is obtained. Several applications escaping the classical framework of convexity are included.
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Blow up of solutions for 3D quasi-linear wave equations with positive initial energy
Author: Amir Peyravi
Abstract: In this paper we investigate blow up property of solutions for a system of nonlinear wave equations with nonlinear dissipations and positive initial energy in a bounded domain in $\mathbb{R}^{3}$. Our result improves and extends earlier results in the literature such as the ones in [Zhou, J. and Mu, C., The lifespan for 3D quasilinear wave equations with nonlinear damping terms, Nonlinear Anal., 74 (2011), 5455--5466] and [Piskin, E., Uniform decay and blow-up of solutions for coupled nonlinear Klein-Gordon equations with nonlinear damping terms, Math. Meth. Appl. Scie., 37 (2014), No. 18, 3036--3047] in which the nonexistence results obtained only for negative initial energy or the one in [Ye, Y., Global existence and nonexistence of solutions for coupled nonlinear wave equations with damping and source terms, Bull. Korean Math. Soc., 51 (2014), No. 6, 1697--1710] where blow up results have been not addressed. Estimate for the lower bound of the blow up time is also given.
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Existence of non-trivial complex unit neighborhoods
Author: Pablo Piniella
Abstract: First, we briefly mention the basic definitions and results on unit neighborhoods of zero. Next, we show the existence of certain non-trivial complex unit neighborhoods of zero. We expose a generalization of the construction method used on the mentioned particular case. Since this construction may not lead to a unit neighborhood of zero, we develop some necessary conditions. Finally, we describe our heuristic use of Wolfram Mathematica to prove the existence of non-trivial complex unit neighborhoods.
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Normality degrees of finite groups
Author: Marius Tărnăuceanu
Abstract: In this paper we introduce and study the concept of normality degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be normal. Explicit formulas are obtained for some particular classes of finite groups. Several limits of normality degrees are also computed.
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Isosceles triple convexity
Author: Liping Yuan, Tudor Zamfirescu and Yue Zhang
Abstract: A set $S$ in $\mathbb{R}^{d}$ is called $it$-convex if, for any two distinct points in $S$, there exists a third point in $S$, such that one of the three points is equidistant from the others. In this paper we first investigate nondiscrete $it$-convex sets, then discuss about the $it$-convexity of the eleven Archimedean tilings, and treat subsequently finite subsets of the square lattice. Finally, we obtain a lower bound on the number of isosceles triples contained in an $n$-point $it$-convex set.
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