University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201$C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions17303184610.22130/scma.2018.59792.211ENArslan Hojat AnsariDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.Tatjana DosenovicFaculty of Technology, Bulevar cara Lazara 1, University of Novi Sad, Serbia.Stojan RadenovicFaculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia.Jeong Sheok UmeDepartment of Mathematics, Changwon National University, Changwon, 641-773, Korea.Journal Article20170224In this paper, we discuss and extend some recent common fixed point results established by using $varphi-$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 generalizes several existing ones<br />in literature.We finally propose three openĀ problems.http://scma.maragheh.ac.ir/article_31846_d6c970ed6b5f3e0d466239bb147f4213.pdf