Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2012; 27(3): 513-522

Printed September 1, 2012

https://doi.org/10.4134/CKMS.2012.27.3.513

Copyright © The Korean Mathematical Society.

Fixed points of occasionally weakly compatible mappings using implicit relation

Badri Datt Pant and Sunny Chauhan

Government Degree College, R. H. Government Postgraduate College

Abstract

In this paper, we prove common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using implicit relation. Our results extend and generalize the results of Altun and Turkoglu [9] in the sense that the concept of occasionally weakly compatible maps is the most general among all the commutativity concepts. Also the completeness of the whole space, continuity of the involved maps and containment of ranges amongst involved maps are completely relaxed.

Keywords: triangle norm (t-norm), Menger space, occasionally weakly compatible maps, implicit relation, fixed point

MSC numbers: Primary 47H10; Secondary 54H25