On $ \gamma $-type contraction principles in $ k $-fuzzy metric spaces

We establish new fixed point results for mappings of $ \gamma $-type in the framework of $ k $-fuzzy metric spaces. Motivated by recent developments on fixed point theory in $ k $-fuzzy metric spaces and by $ \gamma $-type contractions in fuzzy $ S $-metric spaces, we first introduce the notion of a $ k $-fuzzy $ \gamma $-contraction and prove an existence and uniqueness theorem for its fixed point on $ G $-complete $ k $-fuzzy metric spaces. The proof is based on the Picard iteration, a recursive $ \gamma $-inequality, and the $ G $-Cauchy property of the associated sequence in the multi-parameter fuzzy setting. We then propose a more general class of $ k $-fuzzy $ \gamma $-weak contractions, where the contractive condition is expressed in terms of the minimum of three fuzzy proximities involving $ x $, $ \Psi x $, and $ \Psi^2 x $. Along the Picard sequence, we show that the $ \gamma $-weak inequality reduces to a $ \gamma $-contraction-type inequality, which allows us to transfer the strong fixed point principle to the weak setting. In this way, our results simultaneously extend the fixed point theorems for generalized $ k $-fuzzy contractions and provide a multi-parameter generalization of the $ \gamma $-contraction and $ \gamma $-weak contraction principles previously obtained in fuzzy $ S $-metric spaces. Illustrative examples are given to demonstrate the applicability and non-triviality of the proposed conditions.