New fixed point theorem under R-contractions

作者：Roldan Lopez de Hierro Antonio Francisco; Shahzad Naseer

来源：Fixed Point Theory and Applications, 2015, 2015(1): 98.

DOI：10.1186/s13663-015-0345-y

• R-function
• simulation function
• manageable function
• fixed point theorem

In this manuscript we introduce the notions of R-function and R-contractions, and we show an ad hoc fixed point theorem. We prove that this new kind of contractions properly includes the family of all Meir-Keeler contractions and other well-known classes of contractions that have been given very recently (for instance, those using simulation functions and manageable functions). As a consequence, our approach turns out to be appropriate to unify the treatment of different kinds of contractive nonlinear operators.

• 出版日期2015-7-1