在廣義度量空間上之Korovkin型近似定理

Korovkin type approximation theorem in generalized metric space

胡忠堯(Chung-Yao Hu)

指導教授 ： 陳正忠

國立清華大學/理學院/應用數學系所/碩士(2017年)

摘要

本篇論文主要目的是研究關於單值和多值函數的Korovkin型近似定理的結果。對於實數值單值函數的Korovkin型近似定理，我們將討論函數定義在偏度量空間和準度量空間的均勻收斂。對於多值函數的Korovkin型近似定理，我們將討論從偏度量空間均勻收斂到實數中封閉且有界的集合和準度量空間均勻收斂到實數中封閉且有界的集合兩種情形。

關鍵字

Korovkin型近似定理 ； 偏度量空間 ； 準度量空間 ； 多值

並列摘要

The paper is concerned with the result of the Korovkin type approximation theorem related to functions of single-valued and multi-valued. For the study of Korovkin type approximation theorem of single-valued functions, we discuss the uniform convergence in the space of functions define on the space of partial metric and metric-like. As for the Korovkin type approximation theorem of multi-valued functions, we discuss the uniform convergence in the space of functions from partial metric space to closed and bounded sets of real number and the functions from metric-like space to closed and bounded sets of real number.

並列關鍵字

Korovkin type approximation ； partial metric ； metric-like ； multi-valued

參考文獻

[15] Mursaleen, M., and Adem Kilicman. Korovkin Second Theorem via B-Statistical A-Summability. Abstract and Applied Analysis Volume 2013, (2013), Article ID 598963, 6 pages.

[1] Abdullah Alotaibi, and M. Mursaleen. Korovkin type theorems via Lacunary equistatistical convergence. Filomat 30:13, (2016):3641-3647.

[2] Altomare, F. Krovkin-type theorems and approximation by positive linear operators. Surveys in Approximation Theory, (2010):93-105.

[3] Amini-Harandi, A. Metric-like spaces, partial metric spaces and fixed points. Fixed Point Theory and Applications 2012 , (2012):204.

[4] Aydi Hassen, Mujahid Abbas, and Calogero Vetro. Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces. Topology and its Applications, 159.14(2012):3234-3242.