Abstract

Fixed point methods form a cornerstone of contemporary nonlinear analysis. Their systematic study began with Banach’s contraction principle in 1922 [I], which provided a rigorous criterion for the existence and uniqueness of invariant points in metric settings. This landmark idea has since inspired a wide spectrum of investigations, resulting in increasingly generalized frameworks and refined contractive assumptions. In this study, we introduce novel extensions of fuzzy type 𝑇𝐾1- contraction and 𝑇𝐾2 contraction mapping within the context of fuzzy cone metric spaces and establish new fixed point theorems to support these developments.

Keywords

Fuzzy cone metric space, 𝐹𝑢𝑧𝑧𝑦 𝑡𝑦𝑝𝑒 𝑇𝐾1- contraction and 𝐹𝑢𝑧𝑧𝑦 𝑡𝑦𝑝𝑒 𝑇𝐾2 contraction mapping, Fixed point, Common fixed point.

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