A Generalization of Ćirić Quasicontractions

Abstract

We proved a fixed point theorem for a class of maps that satisfy Ćirić's contractive condition dependent on another function. We presented an example to show that our result is a real generalization.

On Interpolative Hardy-Rogers Type Contractions

“…is a standard metric on X. It is natural to define the basic topological concepts, in particular, convergence of a sequence, fundamental (Cauchy) sequence criteria, continuity of the mappings, and completeness of the topological space, in the framework of partial metric spaces; see, for example, [7][8][9][10][11][12][13][14][15][16].…”

Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces

“…is a standard metric on X. It is natural to define the basic topological concepts, in particular, convergence of a sequence, fundamental (Cauchy) sequence criteria, continuity of the mappings, and completeness of the topological space in the framework of partial metric spaces; see, e.g., [8][9][10][11][12][13][14][15][16][17][18].…”

A Discussion on the Existence of Best Proximity Points That Belong to the Zero Set

“…Using (11) and the fact that T is (F, M, ϕ, α p , ψ)−contraction, we obtain F(ρ(ξ n , ξ n+1 ), ϕ(ξ n ), ϕ(ξ n+1 )) = F(ρ(Tξ n−1 , Tξ n ), ϕ(Tξ n−1 ), ϕ(Tξ n )) ≤ α(ξ n−1 , ξ n ) + F(ρ(Tξ n−1 , Tξ n ), ϕ(Tξ n−1 ), ϕ(Tξ n )) ≤ ψ(F(ρ(ξ n−1 , ξ n ), ϕ(ξ n ), ϕ(ξ n+1 ))), for all n ∈ N.…”

“…This notion especially provides some simplicity in computer science, in particular, domain theory. A number of authors have involved in this trend with interesting results, see e.g., [10][11][12][13][14][15][16][17][18] and related reference therein. For the sake of completeness, we recall the concept of partial metric space as follows:…”