Some Fixed-Point Theorems Using C-Class Function in New Abstract Spaces

In this paper, we discuss and extend some recent common fixed point results established by using φ−weakly contractive mappings. A very important step in the development of the fixed point theory was given by A.H. Ansari by the introduction of a C−class function. Using C−class functions, we generalize some known fixed point results. This type of functions is a very important class of functions which contains almost all known type contraction starting from 1922. year, respectively from famous Banach contraction principle. Three common fixed point theorems for four mappings are presented. The obtained results generalize several existing ones in literature .We finally propose three open problems.