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dc.contributor.authorKiran, Quanita-
dc.description.abstractIn [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.en_US
dc.description.sponsorshipHigher Education Commission, Pakistan.en_US
dc.subjectNatural Sciencesen_US
dc.subjectGeneral principles of mathematicsen_US
dc.titleSome generalizations of the Banach fixed point theorem: Single valued and multi-valued mappingsen_US
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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