Uniformly normal structure and uniformly generalized Lipschitzian semigroups
Ahmed Hussein Soliman, Mohamed A. Barakat · The Journal of Nonlinear Sciences and Applications · 2012
In this work, we introduce some condition on one-parameter semigroup of self-mappings it is called \(k\)-uniformly generalized Lipschitzian. The condition is weaker than Lipschitzian type conditions. Also, we show that a \(k\)-generalized Lipschitzian semigroup of nonlinear self-mappings of a nonempty closed convex subset \(C\) of real Banach space \(X\) admits a common fixed point if the semigroup has a bounded orbit and if \(k > 0\). Our results extending the results due to L.C. Ceng, H. K. Xu and J.C. Yao [5]