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

Sattar Alizadeh, Fridoun Moradlou, Peyman Salimi
2014 Filomat  
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
more » ... the obtained results. Notice that above Theorem remains true if the hypothesis on φ is replaced by "φ is lower semi-continuous and φ(t) = 0 if and only if t = 0" (see e.g. [1, 11] ). Recently, Samet et al. [31] introduced the concept of α-ψ-contractive type mappings and established various fixed point theorems for such mappings in complete metric spaces. Very recently, Salimi et al. [30]
doi:10.2298/fil1403635a fatcat:xmqsk7u7wzhwvnjhejbq4cf2ri