Extension and Generalization of Banach Contraction in Metric and in Menger Space

The root of metric fixed point theory is Stefen Banach's contraction mapping, a research source for shrinking the distance between two points in space. As a source, many authors have introduced many contraction mappings as extensions and generalizations of Banach contraction and established fixed point theorems under the property that each such mapping in complete metric and Menger space has a unique fixed point. This article presents updated results of Banach contraction generalization and extension forms in metric and Menger space which helps the comparative and interrelationship study in these spaces.