Abstract:
The aim of this paper is to use the notion of contraction and cyclic contraction mappings to introduce new contraction mappings that don’t imply continuity and prove the existence and uniqueness of fixed point theorems and best proximity point theorems in the settings of complete metric space. An example is provided to illustrate our main result.
Description:
Banach presented a most outstanding result concerning contraction mapping, this famous result is known as the Banach Contraction mapping principle. It states that every contraction mapping on a complete metric space has a unique fixed point. This principle marks the beginning of fixed point theory. Fixed point theory become a subject of great interest due to its application in mathematics and other areas of research. Fixed point theorem in metric spaces plays a significant role in constructing methods to solve problems in mathematics and sciences. Many researchers worked in this area and extended or even generalized the theorem either by considering a more general space imposing some conditions on the domain of the contraction mapping or by considering more general contractive conditions.
