STRONG COUPLED FIXED POINTS AND APPLICATIONS TO FRACTAL GENERATIONS IN FUZZY METRIC SPACES

Abstract

In this paper, we establish a strong coupled fixed-point result for a fuzzy contractive coupling, defined between two subsets of a fuzzy metric space. The coupling is defined by combining the concepts of coupled fuzzy contractions and cyclic mappings. It is the main instrument in the paper. Uniqueness of the strong coupled fixed-point is also shown. There is a corollary and an illustrative example. An example shows that the main theorem properly contains the strong coupled fixed-point result as a corollary. We discuss an application, where construct a special type of Iterated Function System by utilizing a family of fuzzy contractive couplings; this finally leads to the generation of a strong coupled fractal set in fuzzy metric space. A fuzzy version of the Hausdorff distance between compact sets is utilized in the above process. The method of fractal generation is illustrated.

Keywords

• fuzzy metric space
• iterated function system
• coupling
• strong coupled fixed point
• strong coupled fractal