Uniformly normal structure and uniformly generalized Lipschitzian semigroups

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]