A different approach to the fixed point theory by (L,c)-expansion mappings

Abstract

In this study, we introduce a new type of mapping called (L,c)-expansions, induced by a novel class of mappings known as G-functions. These mappings possess the unique property that their moduli may be greater than one, yet they possess unique fixed points. Utilizing Kummer's test, we demonstrate that these (L,c)-expansions can be derived from the well-established framework of Banach contraction mappings. Furthermore, our results allow for the creation of new contractions by altering the type of G-functions used.