Fixed Points Results for $(\alpha, \beta)$ - Contractive Mapping in Intuitionistic Fuzzy Metric-Like Spaces

Abstract

Onbasioglu and Pazar Varol [17] successfully unified metric-like and intuitionistic fuzzy metric structures and establish a foundation for significant advances in fixed-point theory through their introduction of intuitionistic fuzzy metric-like spaces. Building upon this work, we propose a novel class of contraction mappings, called $(\alpha, \beta)$-contraction mappings, within these spaces. Moreover, we contribute to the expanding knowledge base by presenting innovative results related to sequence convergence within this novel framework. We introduce a new concept, namely the $1-\mathcal{M-}$ Cauchy sequence and $1-\mathcal{M-}$ completeness within intuitionistic fuzzy metric-like spaces.

Keywords

• intuitionistic fuzzy (\alpha, \beta) contractive mapping,
• 1 −M−complete intuitionistic fuzzy metric-like spaces
• fixed point

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