Revisiting Fixed Point Results With a Contractive Iterative at a Point

Abstract

In this manuscript, we shall discuss fixed point results with a contractive iterative at a point in the setting of various abstract space. The first aim of this paper is to collect the corresponding basic results on the topic in the literature. After then, our purpose is to combine and connect several existing results in this direction by generalizing the famous theorem of Matkowski. We shall consider some consequence of our main result to illustrate its genuineness. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.