Invariant approximation in 2-banach space with \(H^{+}\) mappings

In order to study the invariant approximation in 2-Banach spaces, we define the concept of \( H^{+} \) $H^{+}$ type nonexpansive mapping to investigate the existence and uniqueness of approximation. Using \( H^{+} \) $H^{+}$ type non expansive multi-valued mapping in 2-Banach spaces to obtain a generalization of the classical Nadler’s fixed point theorem, also discuss the invariant approximation and prove several new results by replacing multi-valued mapping with \( H^{+} \) $H^{+}$ mapping in 2-Banach space.