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In this paper, we introduce the notions of cyclic (α,β)-admissible mappings,  (α,β)-(ψ,Φ)-contractive and weak α - β - ψ - rational contraction mappings  via cyclic (α,β)-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.

Some fixed point results for (α,β)-(ψ,Φ)-contractive mappings