## Real Analysis Exchange

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

### Some types of convergence of sequences of real valued functions.

Ruchi Das and Nikolaos Papanastassiou

#### 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