On one parameter semigroup of self mappings uniformly satisfying expansive Kannan condition (Q432527)

Let \((X, d)\) be a complete bounded metric space. A semigroup \(\{T(t): X\to X\mid t\in G\}\), where \(G\) is a subsemigroup of \([0,+\infty)\), is called uniformly expansive Kannan semigroup if \[ \sup_{t\in G}\Biggl\{\sup_{x,y\in X}\,\Biggl\{{d(T(t)x, T(t)y)\over (d(x,T(t) x)+ d(y, T(t)y)\neq 0}\Biggr\}\Biggr\}= \beta< +\infty. \] In the present paper, the authors prove existence results for fixed points of asymptotically regular uniformly expansive Kannan semigroups (with \(\beta<\sqrt{2}\)) defined on \(X\) with uniform normal structure, which further enjoys a kind of intersection property.