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A Fixed Point Theorem in Fuzzy Metric Spaces using Sub-Compatibility and Sub-Sequential Continuity

Author : Syed Shahnawaz Ali, Jainendra Jain and Mohammed Farooque Khan

Pages : 3692-3696
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Fuzzy Set Theory has seen an extensive growth since the introduction of notion of fuzzy sets by Zadeh in 1965. Kramosil and Michalek introduced the notion of fuzzy metric spaces which was later modified by George and Veeramani and others. The notion of fuzzy metric spaces has very important applications in science and engineering and in particular quantum particle physics. As a result many authors have extended the Banach’s Contraction Principle to fuzzy metric spaces. Fixed point and common fixed point properties for mappings defined on fuzzy metric spaces have been studied by many authors, but most of the properties which provide the existence of fixed points and common fixed points are of linear contractive type conditions. In this Paper, we prove a common fixed point theorem for four self maps in a fuzzy metric space using the concepts of sub compatibility and subsequential continuity introduced by (Bouhadjera et al, 2009).

Keywords: Fuzzy Sets, Fuzzy Metric Space, Semi Compatibility, Weak Compatibility, Reciprocal Continuity, Sub Compatibility, Sub Sequential Continuity, CommonFixed Point.

Article published in International Journal of Current Engineering and Technology, Vol.5, No.6 (Dec-2015)


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