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Fixed point results for Ćirić typeweak contraction in metric spaces with applications to partial metric spaces

Choudhury Binayak S. (Indian Institute of Engineering Science and Technology, Department of Mathematics, Shibpur, Howrah, West Bengal, India)
Kundu A. (Siliguri Institute of Technology, Department of Mathematics, Sukna, Darjeeling, West Bengal, India)
Metiya N. (Bengal Institute of Technology(TIG), Department of Mathematics, Govt. Colony, Kolkata, West Bengal, India)

Partial metric spaces are generalizations of metric spaces which allow for non-zero self-distances. The need for such a definition was felt in the domain of computer science. Fixed point theory has rapidly developed on this space in recent times. Here we define a Ćirić type weak contraction mapping with the help of discontinuous control functions and show that in a complete metric space such a function has a fixed point. Our main result has several corollaries and is supported with examples. One of the examples shows that the corollaries are properly contained in the theorem. We give applications of our results in partial metric spaces.

Keywords: partially ordered set, metric space, partial metric space, Ćirić type weak contraction, control functions, fixed point