On Relative Uniform Convergence of Double Sequences of Functions

摘要

In this paper we have studied the regular relative uniform convergence and relative uniform Cauchy double sequences of functions defined on a compact domain D. We have established that for the double sequences of functions in the complete subset of the set of continuous functions on D, a double sequence is relative uniform convergent if and only if it is relative uniform Cauchy function. We prove some inclusion results involving the different types of relative uniform convergent sequences of functions. To show that the inclusions are proper, we have provided suitable examples. Statement. Chittenden investigated on relative uniform convergence of sequences of functions relative to a scale function in the beginning of 19th century. Again the work in this direction began recently. In this article we investigate the notion of convergence of double sequences of positive linear functions relative to a scale function and investigate some properties.