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Consider a sequence of functions, which are contraction mappings, i.e. for all and for all,. Let be an open, connected subset of. Suppose that uniformly on S and pointwise on. Which of the following is true?

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MCQs on Real Analysis.


Consider a sequence of functions<br><img src='https://www.fatskills.com/images2/GradExams/0CA3AB2D-A3CE-4D3D-A13E-A74D353D5723.png' height='21' width='107'/>, which are contraction mappings, i.e. for all<br><img src='https://www.fatskills.com/images2/GradExams/DF8BB4AB-DA6E-4F72-92D2-5E155E007400.png' height='18' width='71'/> and for all<br><img src='https://www.fatskills.com/images2/GradExams/CAC35A17-2BAE-491A-9F7B-602CF6017AC7.png' height='10' width='11'/>,<br><img src='https://www.fatskills.com/images2/GradExams/62EF7BF6-CD4D-42AE-985F-F4E7050E7F0A.png' height='20' width='205'/>. Let<br><img src='https://www.fatskills.com/images2/GradExams/1094CBF0-312B-479E-918E-9D47176EA119.png' height='15' width='12'/> be an open, connected subset of<br><img src='https://www.fatskills.com/images2/GradExams/AAC87899-60D9-4B95-BD3F-FDE72795CE0D.png' height='18' width='24'/>. Suppose that<br><img src='https://www.fatskills.com/images2/GradExams/B9166F46-86C7-47AF-86DD-0406E1448D9F.png' height='18' width='60'/> uniformly on S and<br><img src='https://www.fatskills.com/images2/GradExams/E18DA6B0-8FD2-4CDE-80E2-9DACE35E2A29.png' height='18' width='59'/> pointwise on<br><img src='https://www.fatskills.com/images2/GradExams/8A84D0CA-A9A9-444A-81B7-5A35F4A75EB0.png' height='18' width='14'/>. Which of the following is true?





 
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