Uniformly normal structure and uniformly generalized Lipschitzian semigroups

Soliman, Ahmed H.¹ ; Barakat, Mohamed A.¹

¹ Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt

Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 5, p. 379-388.

Résumé

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]

Détail

DOI : 10.22436/jnsa.005.05.07

Keywords: Uniformly normal structure, Uniformly generalized semigroup, Fixed point, Characteristic of convexity, Modulus of convexity.

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