Please use this identifier to cite or link to this item: http://prr.hec.gov.pk/jspui/handle/123456789/2421
Title: Some generalizations of the Banach fixed point theorem: Single valued and multi-valued mappings
Authors: Kiran, Quanita
Keywords: Natural Sciences
Mathematics
General principles of mathematics
Algebra
Issue Date: 2010
Publisher: NATIONAL UNIVERSITY OF SCIENCES & TECHNOLOGY, PAKISTAN
Abstract: In [N. Mizoguchi, W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177–188] the authors gave a positive answer to the conjecture of S. Reich concerning the existence of fixed points of multi-valued mappings that satisfy certain contractive conditions. In this paper, we establish some results for multi-valued mappings that satisfy a generalized contractive condition in a way that it contains Mizoguchi’s result as one of its special cases. In addition, our results not only improve the results of Kiran and Kamran [Q. Kiran, T. Kamran, Nadler’s type principle with high order of convergence, Nonlinear Anal. TMA 69 (2008) 4106–4120] and some results of Agarwal et al. [R.P. Agarwal, Jewgeni Dshalalow, Donal O’Regan, Fixed point and homotopy results for generalized contractive maps of Reich type, Appl. Anal. 82 (4) (2003) 329–350] but also provide the high order of convergence of the iterative scheme and error bounds. As an application of our results, we obtain an existence result for a class of integral inclusions.
URI:  http://prr.hec.gov.pk/jspui/handle/123456789//2421
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

Files in This Item:
File Description SizeFormat 
2546S.pdfComplete Thesis2.81 MBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.