Relative uniform convergence of sequence of positive linear Functions

Abstract

The notion of relative uniform convergence of sequences was introduced by E. H. Moore in [An Introduction to a form of general analysis, The New Haven Mathemati- cal Colloquium, Yale University Press, New Haven, 1910]. E. W. Chittenden [Relatively uniform convergence of sequences of functions, Trans. Amer. Math. Soc. 15 (1914), 197-201], made a systematic study of the notion. Then E. W. Chittenden published two more articles in the same journal in the years 1919 and 1922. The area of research re- mained ideal for almost a century. In the beginning of the 21st century, researcher started working on the topic. The work done are from the point of view of convergence of single sequences, the double sequences etc. The main purpose of this chapter is to give a system- atic development of the notion of relative uniform convergence in the field of functions of real variables. As a result of which, researcher may be motivated for further investigation and applications.