EMPLOYING COMMON LIMIT RANGE PROPERTY WITH VARIANTS OF R-WEAKLY COMMUTING MAPPINGS IN METRIC SPACES

SUNNY CHAUHAN, JELENA VUJAKOVIC, SHAMSUL HAQ
2015 The Pure and Applied Mathematics  
The object of this paper is to emphasize the role of 'common limit range property' and utilize the same with variants of R-weakly commuting mappings for the existence of common fixed point under strict contractive conditions in metric spaces. We also furnish some interesting examples to validate our main result. Our results improve a host of previously known results including the ones contained in Pant [Contractive conditions and common fixed points, Acta Math. Acad. Paedagog. Nyházi. (N.S.) 24
more » ... . Nyházi. (N.S.) 24 (2) (2008) , 257-266 MR2461637 (2009h:54061)]. In the process, we also derive a fixed point result satisfying φ-contractive condition. Primary 47H10, Secondary 54H25. Key words and phrases. metric space, R-weakly commuting mappings, R-weakly commuting mappings of type (A g ), R-weakly commuting mappings of type (A f ), R-weakly commuting mappings of type (P ), property (E.A), common limit range property, fixed point.
doi:10.7468/jksmeb.2015.22.2.127 fatcat:ubffxrpppbhrvdoqq5kw3w6m6u