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 Communications in Advanced Mathematical SciencesNumber of Followers: 0     Open Access journal ISSN (Print) 2651-4001 Published by DergiPark  [201 journals]
• On Growth and Approximation of Generalized Biaxially Symmetric Potentials
on Parabolic-Convex Sets

• Authors: Devendra Kumar
Abstract: The regular, real-valued solutions of the second-order elliptic partial differential equation\beq \frac{\prt^2F}{\prt x^2} + \frac{\prt^2F}{\prt y^2} + \frac{2\alpha+1}{x} \frac{\prt F}{\prt y} + \frac{2\beta+1}{y} \frac{\prt F}{\prt x} =0, \alpha,\beta>\frac{-1}{2}\eeq are known as generalized bi-axially symmetric potentials (GBSP's). McCoy \cite{17} has showed that the rate at which approximation error $E^{\frac{p}{2n}}_{2n}(F;D),(p\ge 2,D$ is parabolic-convex set) tends to zero depends on the order of $GBSP$ F and obtained a formula for finite order. If $GBSP$ F is an entire function of infinite order then above formula fails to give satisfactory information about the rate of decrease of $E^{\frac{p}{2n}}_{2n}(F;D)$. The purpose of the present work is to refine above result by using the concept of index-q. Also, the formula corresponding to $q$-order does not always hold for lower $q$-order. Therefore we have proved a result for lower $q$-order also, which have not been studied so far.
PubDate: Mon, 24 Dec 2018 00:00:00 +030

• L-Fuzzy Invariant Metric Space

• Authors: Servet Kütükçü
Abstract: In this paper, we define L-fuzzy invariant metric space, and generalize some well known results in metric and fuzzy metric space including Uniform continuity theorem and Ascoli-Arzela theorem.
PubDate: Mon, 24 Dec 2018 00:00:00 +030

• On Bicomplex Pell and Pell-Lucas Numbers

• Authors: Fügen Torunbalcı Aydın
Abstract: In this paper, bicomplex Pell and bicomplex Pell-Lucas numbers are defined. Also, negabicomplex Pell and negabicomplex Pell-Lucas numbers are given. Some algebraic properties of bicomplex Pell and bicomplex Pell-Lucas numbers which are connected between bicomplex numbers and Pell and Pell-Lucas numbers are investigated. Furthermore, d'Ocagne's identity, Binet's formula, Cassini's identity and Catalan's identity for these numbers are given.
PubDate: Mon, 24 Dec 2018 00:00:00 +030

• Norm-Attainability and Range-Kernel Orthogonality of Elementary Operators

• Authors: Bernard Okelo
Abstract: Various aspects of elementary operators have been characterized by many mathematicians. In this paper, we consider norm-attainability and orthogonality of these operators in Banach spaces. Characterizations and generalizations of norm-attainability and orthogonality are given in details. We first give necessary and sufficient conditions for norm-attainability of Hilbert space operators then we give results on orthogonality of the range and the kernel of elementary operators when they are implemented by norm-attainable operators in Banach spaces.
PubDate: Mon, 24 Dec 2018 00:00:00 +030

• On the Periodic Solutions of Some Systems of Difference Equations

• Authors: E. M. Elsayed; H. S. Gafel
Abstract: In this paper, we study the solution of the systems of difference equations \begin{equation*} x_{n+1}=\frac{1\pm (y_{n}+x_{n-1})}{y_{n-2}},\ \ \ y_{n+1}=\frac{1\pm (x_{n}+y_{n-1})}{x_{n-2}},\;\;n=0,1,..., \end{equation*}% {\Large \noindent }where the initial conditions $x_{-2},\ x_{-1},\ x_{0},$ $% y_{-2},\ y_{-1},\ y_{0}$ are arbitrary non zero real numbers.
PubDate: Mon, 24 Dec 2018 00:00:00 +030

• Modifications of Strongly Nodec Spaces

Abstract: In this paper, we introduce the notion of strongly nodec spaces and study their properties. Also, we discuss strongly nodec generalized metric spaces. Furthermore, we extend these notions to $T_{0}$-strongly nodec space by using the quotient map.
PubDate: Mon, 24 Dec 2018 00:00:00 +030

• Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach

• Authors: Luis Gerardo Mármol; Carmen Judith Vanegas
Abstract: In this paper we study certain systems of mixed-type functional differential equations, from the point of view of the $C_{0}$-semigroup theory. In general, this type of equations are not well-posed as initial value problems. But there are also cases where a unique differentiable solution exists. For these cases and in order to achieve our goal, we first rewrite the system as a classical Cauchy problem in a suitable Banach space. Second, we introduce the associated semigroup and its infinitesimal generator and prove important properties of these operators. As an application, we use the results to characterize the null controllability for those systems, where the control $u$ is constrained to lie in a non-empty compact convex subset $\Om{}$ of $\R^n$.
PubDate: Mon, 24 Dec 2018 00:00:00 +030

• Fixed Point Sets of Multivalued Contractions and Stability Analysis

• Authors: Nikhilesh Metiya; Binayak S. Choudhury, Sunirmal Kundu
Abstract: In this paper we derive a fixed point result for a multivalued generalized almost contraction which contains several rational terms through a six variables function and a four variables function. The space is assumed to satisfy some regularity conditions. In another part of the paper we establish stability results for fixed point sets of these contractions. The corresponding singlevalued case is also discussed. The results are obtained without any assumption of continuity. There are two illustrative examples.
PubDate: Mon, 24 Dec 2018 00:00:00 +030

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