- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 7 Issue: 1
- New classes of control functions for nonlinear contractions and applications
New classes of control functions for nonlinear contractions and applications
Authors : Maher BERZİG
Pages : 29-40
Doi:10.31197/atnaa.1134524
View : 767 | Download : 288
Publication Date : 2023-03-31
Article Type : Research Article
Abstract :We initiate the use of sub and super homogeneous control functions for nonlinear contractions in complete metric spaces and establish new fixed point theorems. Moreover, we develop other variants of control functions for the fixed point theorems of Boyd-Wong [2] and Matkowski [3]. As application, we present new sufficient conditions ensuring the existence of solutions to some classes of integral equations of Fredholm and Volterra type.Keywords : Fixed Point Theorems, Contraction-type mappings, Fredholm and Volterra integral equations