SUZUKI’S THEOREM ON S(q1,q2,q3)-METRIC SPACES

Abstract

This paper extends the Suzuki theorem, a generalization of the Banach contraction principle, to a new class of generalized metric spaces, specifically S(q1, q2, q3)-metric spaces. The primary objective of this study is to establish the necessary conditions to affirm the unique existence of fixed points for mappings satisfying the Suzuki contraction condition on S(q1, q2, q3)-metric spaces. Let (X, S, q1, q2, q3) be a complete S(q1, q2, q3)-metric space, q = max{q1 + q2, q3²} and T: X → X be a mapping; we define a function θ(r) ≤ 1 for all r ∈ [0, 1/q²) satisfying θ(r)d(x, Tx) ≤ d(x, y) ⇒ d(Tx, Ty) ≤ r d(x, y)/q³ for all x, y ∈ X, then there exists a unique fixed point z of T. The results of this paper indicate that the Suzuki theorem remains valid in generalized metric spaces, specifically in S(q1, q2, q3)-metric spaces.