Fixed Point of Single-Valued Cyclic Weak $\varphi_F$−Contraction Mappings

Sirous Moradi

Fixed point results are presented for single-valued cyclic weakly $\varphi_F$-contractive mappings on complete metric spaces $(X,d)$, where $\varphi[0,+1)\to[0,+1)$ is a function with $\varphi^−1(0)=\{0\}$, $\varphi(t)<t$ for all $t>0$ and $\varphi(t_n)\to0$ implies $t_n\to0$, and $F:[0,+1)\to[0,+1)$ is continuous with $F^−1(0)=\{0\}$ and $F(t_n)\to0$ implies $t_n\to0$. Our results extend previous results given by Rhoades (2001)[15], Moradi and Beiranvand (2010)[8], Amini-Harandi (2010)[2] and Karapinar (2011)[6].