Abstract
We establish fixed point, stability and genericity theorems for strict contractions on complete metric spaces with graphs.
Highlights
For nearly sixty years there has been a lot of research activity regarding the fixed point theory of nonexpansive and contractive mappings
We identify the graph G with the pair (V ( G ), E( G ))
Let all the assumptions of Theorem 1 hold, let the mapping T be continuous as a self-mapping of ( X, ρ) and let x∗ ∈ X be as guaranteed by Theorem 1 and satisfy x ∗ = T ( x ∗ )
Summary
[1,2,3,4,5,6,7,8,9,10,11,12,13,14] and references cited therein This activity stems from Banach’s classical theorem [15] concerning the existence of a unique fixed point for a strict contraction. It concerns the convergence of (inexact) iterates of a nonexpansive mapping to one of its fixed points. The study of nonexpansive and contractive mappings on complete metric spaces with graphs has recently become a rapidly growing area of research.
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