Search

Abstract: In this paper, we introduce a new class of algebras satisfying certain conditions which has been named power algebras and we prove some fixed point theorems for a new class of contractions. We give new conditions for the existence and uniqueness of fixed points for this new class of mappings which are not a contraction in the usual algebra. Also, we introduce a new iterative algorithm for fixed-point problems in a Banach algebra. This results improve and extend the corresponding conclusions of the Ishikawa algorithm under weaker conditions and lead to stronger results. In conclusion, we give an application to nonlinear integral equations.

In this paper we present some coupled coincidence point results for a class of contractive mappings in the setup of partially ordered $$G$$ G -metric space. Adding few appropriate conditions, common coupled fixed points are obtained. We also provide examples to illustrate the results presented herein.