A NEW MODIFIED AVERAGING IMPLICIT ITERATION
PROCESS WITH ERRORS FOR COMMON FIXED POINTS
OF A FINITE FAMILY OF ASYMPTOTICALLY
DEMICONTRAC-TIVE MAPS IN
ARBITRARY REAL BANACH SPACES

U.S. Jim, Z. Ongodiebi, F.A. Efiong
Department of Mathematics and Statistics
University of Uyo
P.M. B 1017, Uyo, NIGERIA

Abstract. In this paper, the implicit and explicit iteration process with errors recently introduced by Gu (An. St. Univ. Ovidius Constanta 18(1), 2010, 139-154) has been used to approximate the common fixed points of a finite family of asymptotically demicontractive maps in arbitrary real Banach spaces. These results extend, generalize and complement the results of Gu [4], Su and Li [13], Jim [11], Igbokwe and Jim [3] and extend several others from the class of asymptotically demicontractive maps to the more general class of asymptotically demicontractive maps (see for example [5], [7] and [9]).

Received: December 12, 2011

AMS Subject Classification: 47H10, 37C25, 55M20

Key Words and Phrases: asymptotically demicontractive, composite implicit iteration, fixed point, uniformly Lipschitzian, Banach spaces

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