IJPAM: Volume 78, No. 3 (2012)

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

U.S. Jim$^1$, Z. Ongodiebi$^2$, F.A. Efiong$^3$
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 $\phi-$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 $\phi-$demicontractive maps (see for example [5], [7] and [9]).

Received: December 12, 2011

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

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

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 3