Fixed Point Results for Implicit Kannan-Type Contractions in \(2\)-Modular Spaces under the \(\Delta_{2}\)-Condition

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In this paper, we study implicit Kannan-type contractions in non-convex and \(\rho\)-complete \(2\)-modular spaces. The class under consideration unifies modular Kannan-type contractions and certain generalized involutions satisfying an implicit contractive condition. Under the \(\Delta_{2}\)-condition with \(\Delta_{2}\)-constant \(\kappa\in(1,2)\), which is incompatible with the convexity of the \(2\)-modular, we establish the existence and uniqueness of a fixed point by means of a Krasnosel’skiĭ–Mann iterative scheme. As an application, we obtain a coincidence point theorem for commuting involutions.

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