Suzuki-type fixed point theorem in \(S_N\)-metric spaces: A strong \(b\)-metric approach

Abstract. In this paper, we introduce the concept of \(S_N\)-metric spaces, which naturally generalizes metric and \(S\)-metric spaces. By constructing an induced strong \(b\)-metric \(R(x,y) = D(x, \ldots, x, y)\), we show that every \(S_N\)-metric space naturally induces a strong \(b\)-metric space with coefficient \(q = N - 1\). Based on this structural connection, we first establish a Suzuki-type fixed point theorem in strong \(b\)-metric spaces and subsequently derive the corresponding result in \(S_N\)-metric spaces as a direct consequence. Non-trivial examples are also provided to illustrate our main result.

Key words and phrases. Suzuki, fixed point, strong \(b\)-metric spaces, \(S_N\)-metric spaces.