Fixed point theorems for Kikkawa-Suzuki type multivalued operators in gauge spaces

Let η : [0, 1[ → # 1 2 , 1 # be a function defined by η(a) := 1 1 + a . Let (X, d) be a metric space and Y ⊆ X. Then, F : Y → Pb,cl(X) is called an a−KS multivalued operator if a ∈ [0, 1[ and x, y ∈ Y with η(a) · D(x, F(x)) ≤ d(x, y) implies H(F(x), F(y)) ≤ a · d(x, y). Kikkawa and Suzuki recently proved in [5] that if F is an a−KS multivalued operator in a complete metric space then F has a fixed point. The aim of this article is to extend their results to gauge spaces.