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International Journal of Mathematics and Mathematical Sciences
Volume 21, Issue 4, Pages 677-680
http://dx.doi.org/10.1155/S0161171298000933

Fixed points of a certain class of mappings in spaces with uniformly normal structure

1Department of Mathematics, Dong-A University, Pusan 607-714, Korea
2Govt. B. H. S. S. Gariaband, Dist. Raipur, 493889, M. P., India
3Govt. H. S. S. Kumhari, Dist. Durg, 490042, M. P., India

Received 12 September 1996; Revised 4 May 1997

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A fixed point theorem is proved in a Banach space E which has uniformly normal structure for asymptotically regular mapping T satisfying: for each x,y in the domain and for n=1,2,,TnxTnyanxy+bn(xTnx+yTny)+cn(xTny+yTny), where an,bn,cn are nonnegative constants satisfying certain conditions. This result generalizes a fixed point theorem of Górnicki [1].