Abstract. The Banach contraction principle plays a very important role in nonlinear analysis and has many genralizations. Recently Suzuki (2008) gave a new generalization. Then, his method was extended by Kikkawa and Suzuki (2008). 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. In this paper, some results (Theorem 3.1 and Theorem 3.4 and their corollaries) in this direction concerning (common) fixed point theorems for generalized contractive multivalued mappings are presented using a result of Bose and Mukherjee(1977) which extend the results obtained by Bose and Mukherjee, Bose and Roychowdhury (with some constraint), Singh and Mishra, Kikkawa and Suzuki, Mot and Petrusel and others. In Theorem 3.7, a coincidence point theorem for a hybrid pair of mappings f:X→X and T:X→CB(X) is presented.

Received: September 17, 2012

AMS Subject Classification: 47H10, 47H04, 54H25

Key Words and Phrases: common fixed point, coincidence point, contractive multifunction, Hausdorff metric

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