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Abstract and Applied Analysis
Volume 2014, Article ID 683295, 6 pages
Research Article

Implicit Approximation Scheme for the Solution of -Positive Definite Operator Equation

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21859, Saudi Arabia
2Department of Mathematics, Lahore Leads University, Lahore 54810, Pakistan
3Departement of Mathematics, University of Botswana, Private Bag Box 00704, Gaborone, Botswana

Received 5 December 2013; Accepted 9 February 2014; Published 23 March 2014

Academic Editor: Ljubomir B. Ćirić

Copyright © 2014 Naseer Shahzad et al. 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.


We construct an implicit sequence suitable for the approximation of solutions of K-positive definite operator equations in real Banach spaces. Furthermore, implicit error estimate is obtained and the convergence is shown to be faster in comparsion to the explicit error estimate obtained by Osilike and Udomene (2001).