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In this paper, we explore the framework of -metric space, a well-known generalization of metric spaces, and establish fixed point results for -- contractive mappings in a complete -metric spaces endowed with L-fuzzy mappings. These additions broaden the body of knowledge in fixed point theory and fuzzy mappings. We showcase the practical applicability of our proposed results through illustrative examples and also, explore as an application, the solution for fuzzy initial-value problems.
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