二元函數(shù)列的收斂性研究論終稿畢業(yè)論文-wenkub
2023-07-08 08:18:39 本頁面
【正文】 間的一個開覆蓋，則從中可選出有限個開區(qū)間來覆蓋([5])。 設(shè)函數(shù)列與函數(shù)定義在同一數(shù)集上，對每一固定的任給正數(shù)恒存在正數(shù)，使得當(dāng)時總有則稱函數(shù)列收斂于([4])。以一元函數(shù)列的一致收斂性為基礎(chǔ)，給出了二元函數(shù)列的一致收斂性判別法，也通過正反對比的例題加深理解二元函數(shù)列的收斂概念。通過類比方法討論了二元函數(shù)列的性質(zhì), 給出了相應(yīng)的一些例子。函數(shù)列的一致收斂性通常應(yīng)用在微分方程求解理論研究，經(jīng)濟控制理論，人口控制理論，函數(shù)項級數(shù)的收斂性研究，含參變量積分計算，近似計算與誤差估計等方面。提出了判定二元函數(shù)列一致收斂的柯西準(zhǔn)則和二元函數(shù)列的極限函數(shù)連續(xù)、可導(dǎo)及可積的充分條件。引進了二元函數(shù)列一致收斂、局部一致收斂與次一致收斂的概念。函數(shù)列的一致收斂性概念在微分方程求解理論，控制理論，近似計算與誤差估計等方面有重要應(yīng)用。本文研究二元函數(shù)列的收斂性。通過類比方法討論了二元函數(shù)列的性質(zhì), 給出了相應(yīng)的一些例子。關(guān)鍵詞：二元函數(shù)列，一致收斂，次一致收斂，局部一致收斂，收斂性判別法 AbstractThe theory of function sequence’s convergence is one of important contents in mathematics analysis. The notion of the uniform convergence of function sequences has been applied to the theoretical research of solving differential equations, the theory of control, approximation pution and the estimation of errors, and so on. The convergence of bivariate function sequences is investigated in this article. First，some definitions and theorems for univariate function sequences are recalled. Next, the notion of bivariate function sequences is proposed. The uniform convergence, the local uniform convergence and the subuniform convergence of bivariate function sequences are introduced. By using analogy method we discussed the properties of bivariate function sequences, and provide some corresponding examples. The implication relations among the local uniform convergence, the subuniform convergence and the uniform convergence of bivariate function sequences are investigated. By analogy to the conditions of uniform convergence of the univariate function sequences, we present the sufficient and necessary conditions for the uniform convergence of bivariate function sequences. Several constructive examples are given to for us to explain the theorems. Cauchy criteria for uniform convergence of bivariate function sequences is proposed. The sufficient conditions of the continuity, the differentiability, the integrability of limit functions of bivariate function seque
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