Real Analysis Exchange

Some types of convergence of sequences of real valued functions.

Ruchi Das and Nikolaos Papanastassiou

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Abstract

Using the notions of uniform equal and uniform discrete convergence for sequences of real valued functions, the classes of functions which are uniform equal limits and uniform discrete limits of sequences of real valued functions belonging to certain class are studied. Also, new types of convergence of sequences of real valued functions, called $\alpha$-uniform equal, $\alpha$-strong uniform equal and $\alpha$-equal are defined and studied. Using $\alpha$-uniform equal convergence, a characterization of compact metric space is obtained.

Article information

Source
Real Anal. Exchange, Volume 29, Number 1 (2003), 43-59.

Dates
First available in Project Euclid: 9 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149860181

Mathematical Reviews number (MathSciNet)
MR2061292

Zentralblatt MATH identifier
1069.26003

Subjects
Primary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 26A03: Foundations: limits and generalizations, elementary topology of the line

Keywords
Uniform equal convergence uniform discrete convergence continuous convergence $\alpha$-u.e. convergence $\alpha$-e. convergence $\alpha$- s.u.e. convergence ordinary class

Citation

Das, Ruchi; Papanastassiou, Nikolaos. Some types of convergence of sequences of real valued functions. Real Anal. Exchange 29 (2003), no. 1, 43--59. https://projecteuclid.org/euclid.rae/1149860181


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