Let {fn}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{f_n\}$$\end{document} be a sequence of meromorphic functions defined in a domain D, and let {psi n}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{\psi _n\}$$\end{document} be a sequence of holomorphic functions on D, whose zeros are multiple, such that psi n ->psi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi _n\rightarrow \psi $$\end{document} converges locally uniformly in D, where psi(not equivalent to 0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi (\not \equiv 0)$$\end{document} is holomorphic in D. If, (1) fn not equal 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_n\ne 0$$\end{document} and fn(k)not equal 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_n<^>{(k)}\ne 0$$\end{document};(2) all zeros of fn(k)-psi n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepa
Let {fn} be a sequence of functions meromorphic in a domain D, let {hn} be a sequence of holomorphic functions in D, such that hn（z） x h（z）, where h（z） 0 is holomorphic in D, and let k be a positive integ...
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Let {fn} be a sequence of functions meromorphic in a domain D, let {hn} be a sequence of holomorphic functions in D, such that hn（z） x h（z）, where h（z） 0 is holomorphic in D, and let k be a positive integer. If for each n ∈ N＋, fn（z） ≠ 0 and fn（k）（z） - hn（z） has at most k distinct zeros （ignoring multiplicity） in D, then {fn} is normal in D.
In this work, we discuss various kinds of I-uniform convergence for sequences of functions and introduce the concepts of I*-uniform convergence, I and I*-uniformly Cauchy sequences of functions in 2-normed spaces. The...
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In this work, we discuss various kinds of I-uniform convergence for sequences of functions and introduce the concepts of I*-uniform convergence, I and I*-uniformly Cauchy sequences of functions in 2-normed spaces. Then, we show the relationships between them.
We investigate the classes of ideals for which the Egoroff's theorem or the generalized Egoroff's theorem holds between ideal versions of pointwise and uniform convergences. The paper is motivated by considera...
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We investigate the classes of ideals for which the Egoroff's theorem or the generalized Egoroff's theorem holds between ideal versions of pointwise and uniform convergences. The paper is motivated by considerations of Korch (Real Anal Exchange 42(2):269-282, 2017).
The purpose of this research study is to understand how math majors conceptualize and make sense of pointwise convergence of sequence of functions in a series of in-depth qualitative interviews. Framed in APOS (Dubins...
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The purpose of this research study is to understand how math majors conceptualize and make sense of pointwise convergence of sequence of functions in a series of in-depth qualitative interviews. Framed in APOS (Dubinsky & McDonald, 2002) and VA (visual-analytic) strategy coordination (Zazkis, Dubinsky & Dautermann, 1996) theoretical perspectives, the analysis showed that students demonstrated a diversity of mathematical behaviors associated mostly with the process level of understanding in APOS model. Yet a complete understanding of pointwise convergence at object level did not take place, students still also exhibited significant achievements in progression from process to object. The VA coordination also proved a beneficial mechanism in students' making sense of pointwise convergence in a dynamic geometry environment.
In this paper we study lacunary statistical convergence of sequences of functions in intuitionistic fuzzy normed spaces. We define concept of lacunary statistical pointwise convergence and lacunary statistical uniform...
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In this paper we study lacunary statistical convergence of sequences of functions in intuitionistic fuzzy normed spaces. We define concept of lacunary statistical pointwise convergence and lacunary statistical uniform convergence in intuitionistic fuzzy normed spaces and we give some basic properties of these concepts.
This paper presents some methods for constructing new resilient functions from old ones. These methods are significant generalizations of some previously known methods. Furthermore, we construct some infinite families...
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ISBN:
(纸本)9781424439867
This paper presents some methods for constructing new resilient functions from old ones. These methods are significant generalizations of some previously known methods. Furthermore, we construct some infinite families of resilient functions with optimal nonlinearity which is particularly well-suited for combining linear feedback shift registers.
In this article we characterize the discrete limits of sequences of piece-wise linear functions. A function f : [0, 1] -> R is the discrete limit of a sequence of piecewise linear functions iff there are closed set...
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In this article we characterize the discrete limits of sequences of piece-wise linear functions. A function f : [0, 1] -> R is the discrete limit of a sequence of piecewise linear functions iff there are closed sets A(n) such that [0, 1] = U-n A(n) and the restricted functions f/A(n) are linear.
Our goal is to study quantities in Riemannian geometry which remain invariant under the conformal change of metrics that is, under changes of metrics which stretch the length of vectors but preserve the angles between...
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Our goal is to study quantities in Riemannian geometry which remain invariant under the conformal change of metrics that is, under changes of metrics which stretch the length of vectors but preserve the angles between any pair of vectors. We call such a quantity conformally invariant . In conjunction with the study of conformal invariants, we are also interested in studying conformally covariant operators , that is, linear dierential operators dened on a manifold which prescribes the change of a geometric quantity under conformal change of metrics.
The aim of the paper is to characterize the class of sets of points at which a sequence of real functions of a distinguish family ℱ⊂ℝX discretely converges.
The aim of the paper is to characterize the class of sets of points at which a sequence of real functions of a distinguish family ℱ⊂ℝX discretely converges.
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