Jachymski [ Proc. Amer. Math. Soc., 136 (2008), 1359-1373] gave modified version of a Banach fixed point theorem on a metric space endowed with a graph. In the present paper, (G, Φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. Also, Hardy-Rogers G-contraction have been introduced and some fixed point theorems have been proved. S...

We prove the following generalization of Cartwright–Littlewood fixed point theorem. Suppose h : R 2 → is an orientation preserving planar homeomorphism, and X acyclic continuum. Let C be a component ∩ ( ) . If there c ∈ such that O + ⊆ or − then also contains Our result generalizes earlier results Ostrovski Boroński, answers Question from Boroński (2017). The proof inspired by short Cartwright ...