IJPAM: Volume 92, No. 4 (2014)
FOR MULTI-VALUED MAPPINGS AND APPLICATIONS
Department of Mathemtics
University of Texas-PanAmerican
Edinburg, Texas 78539, USA
Abstract. Recently Suzuki (2008) and then Kikkawa and Suzuki (2008) gave a new generalization of the Banach contraction principle. Then, Mot and Petrusel (2009), Dhompapangasa and Yingtaweesttikulue (2009), Bose and Roychowdhury (2011), Singh and Mishra (2010), and Doric and Lazovic (2011) further extended their work. Recently Bose (2012) obtained some Suzuki-type common fixed point theorems for generalized contractive multivalued mappings using a result of Bose and Mukherjee(1977) which extend the previously obtained results.
Recently Damjanovic and Doric(2011) obtained a multivalued generalization
of theorems Kikkawa and Suzuki (2008) concerning Kannan mappings.
Also Singh and Mishra (2010) considered coincidence and fixed point
theorems for a class of hybrid pair of single-valued and multi-valued
maps in metric space setting and Singh et al (2012) prsented a common
fixed point theorem for a pair of multi-valued maps in a complete
metric space extending a recent theorem of Doric and Lazovic. First
we generalize the theorem of Singh et al which also extend the theorem
of Singh and Mishra(2010). Then we extend the theorem of Damjanovic
and Doric to a common fixed point theorem of a pair of multivalued
mappings. As an application, we consider the existence of a common
solution for a class of functional equations arising in dynamic programming.
Received: August 3, 2013
AMS Subject Classification: 47H10, 47H04, 54H25
Key Words and Phrases: common fixed point, coincidence point, contractive multifunction, Hausdorff-Pompeiu metric
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DOI: 10.12732/ijpam.v92i4.4 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 481 - 497
This work is licensed under the Creative Commons Attribution International License (CC BY).