Common fixed points of minimal contractive conditions in intuitionistic fuzzy metric space

Article type: Research Article

Authors: Manro, Saurabh | Bisht, Ravindra K.

Affiliations: School of Mathematics and Computer Applications, Thapar University, Patiala (Punjab), India | Department of Mathematics-Applied Sciences & Humanities, Bipin Triphati Kumaon Institute of Technology, Dwarahat, Almora, India

Note: [] Corresponding author. Saurabh Manro, School of Mathematics and Computer Applications, Thapar University, Patiala (Punjab), India. E-mail: sauravmanro@hotmail.com

Abstract: The purpose of the present paper is to prove some new common fixed point theorems in intuitionistic fuzzy metric spaces for a pair of self-mappings satisfying minimal type contractive and continuity conditions. Our results substantially generalize and improve a multitude of relevant common fixed point theorems of the existing literature in metric as well as intuitionistic fuzzy metric spaces. We also provide an affirmative answer in the settings of intuitionistic fuzzy metric space to the open problem posed by Rhoades [28] regarding existence of a contractive definition which is strong enough to generate a fixed point, but which does not force the map to be continuous at the fixed point.

Keywords: Compatible maps, weaker continuity condition, intuitionistic fuzzy metric space, common fixed point

DOI: 10.3233/IFS-131034

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 2, pp. 761-768, 2014