IJPAM: Volume 92, No. 4 (2014)


Ramendra Krishna Bose
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?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 92
Issue: 4
Pages: 481 - 497

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).