Uniformly normal structure and uniformly generalized Lipschitzian semigroups


Authors

Ahmed H. Soliman - Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt. Mohamed A. Barakat - Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt.


Abstract

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]


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ISRP Style

Ahmed H. Soliman, Mohamed A. Barakat, Uniformly normal structure and uniformly generalized Lipschitzian semigroups, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 5, 379--388

AMA Style

Soliman Ahmed H., Barakat Mohamed A., Uniformly normal structure and uniformly generalized Lipschitzian semigroups. J. Nonlinear Sci. Appl. (2012); 5(5):379--388

Chicago/Turabian Style

Soliman, Ahmed H., Barakat, Mohamed A.. "Uniformly normal structure and uniformly generalized Lipschitzian semigroups." Journal of Nonlinear Sciences and Applications, 5, no. 5 (2012): 379--388


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