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Common fixed point theorems for variants of R-weakly commuting mappings in topologically complete tychonoff (uniform) spaces

Kohli J. K., Kumar D.

Demonstratio Mathematica

2012

Vol. 45, nr 1

169-178

Three variants of R-weakly commuting mappings in the realm of uniform spaces are defined. Examples are included to reflect upon the distinctiveness of the notions so defined. Common fixed point theorems concerning these variants of R-weakly commuting mappings in the framework of uniform spaces are obtained. This generalizes several known results in the literature including those of Granas and Dugundji [3], Tarafdar [12] and others. Moreover, as a bi-product we obtain several common fixed point theorems which are well in contrast with a common fixed point theorem of Jungck [4] who proved the same for commuting mappings.