Some Fixed Point Results for $(\alpha,\beta)$-$(\psi,\varphi)$-Contractive Mappings

Sattar Alizadeh, Fridoun Moradlou, Peyman Salimi

In this paper, we introduce the notions of cyclic $(\alpha,\beta)$-admissible mappings, $(\alpha,\beta)$-$(\psi,\varphi)$-contractive and weak $\alpha$-$\beta$-$\psi$-rational contraction mappings via cyclic $(\alpha,\beta)$-admissible mappings. We prove some new fixed point results for such mappings in the setting of complete metric spaces. The obtained results generalize, unify and modify some recent theorems in the literature. Some examples and an application to integral equations are given here to illustrate the usability of the obtained results.