Abstract
Since proving many fixed point theorems in a given space requires either growing the space itself or growing the self-mapping that works on it, both of these options are good. The operators' ideal generated by a weighted binomial matrix in the Nakano sequence space of extended s-fuzzy functions is constructed. Some structures for it based on geometry and topology are presented. It has been proven that the Kannan contraction operator has a unique fixed point in this class. Lastly, sufficient conditions such that a fuzzy non-linear matrix system of Kannan-type has a unique solution in this ideal class are investigated and a numerical example to explain our results are given.
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