Remarks on certain selected fixed point theorems

Remarks on Certain Selected Fixed Point Theorems

Theorem 1. Let A, S, I, and J be self-mappings of a complete metric space (X,d) such that the pairs (A,I) and (S,J) are commuting and A(X)⊂ J(X) and S(X)⊂ I(X) such [ 1+pd(Ax,Sy)]d(Ix,Jy) ≤ pmax{d(Ix,Ax)·d(Sy,Jy),d(Ix,Sy)·d(Jy,Ax)} +φ(d(Ax,Sy),d(Ix,Ax),d(Sy,Jy),d(Ix,Sy),d(Jy,Ax)), (1) for all x,y ∈ X where p ≥ 0 and φ ∈ Ψ . Then A, S, I, and J have a unique common fixed point provided one of th...

Remarks on Recent Fixed Point Theorems

Remarks on the Paper ``Coupled Fixed Point Theorems for Single-Valued Operators in b-Metric Spaces''

In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...

Remarks on Lipschitzian Mappings and Some Fixed Point Theorems

Let X, Y be the normed spaces, C ⊂ X a convex set, and T : C → Y a continuous mapping. Some weak conditions implying the Lipschitz continuity of T are presented. Applications to the fixed point theory and theory of composition operators are presented.

Remarks onG-metric spaces and fixed point theorems