Fuzzy metric approach to \((\kappa,\alpha,\beta)\)-interpolative Kannan type cyclic contractions and nonlinear integral equations

Abstract

In this paper, we introduce a new class of \((\kappa,\alpha,\beta)\)-interpolative Kannan type cyclic contractions in fuzzy metric spaces. By extending the recently introduced fuzzy \((\kappa,\alpha,\beta)\)-interpolative Kannan contractions to the cyclic setting, we establish existence and uniqueness results for fixed points under suitable assumptions. The obtained results generalize and unify several well-known fixed point theorems in the existing literature. Illustrative examples are provided to demonstrate the applicability of the proposed results.