Fixed Point Theory and Applications (Jan 2010)

On Uniformly Generalized Lipschitzian Mappings

  • Ahmed H. Soliman,
  • M. Imdad

DOI
https://doi.org/10.1155/2010/692401
Journal volume & issue
Vol. 2010

Abstract

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We consider another class of generalized Lipschitzian type mappings and utilize the same to prove fixed point theorems for asymptotically regular and uniformly generalized Lipschitzian one-parameter semigroups of self-mappings defined on bounded metric spaces equipped with uniform normal structure which yield corresponding results in respect of semigroup of iterates of a self-mapping as corollaries. Our results also generalize some relevant results due to the work of Lim and Xu (1995), Yao and Zeng (2007), and Soliman (2009).