... Fixed point theorem (I) In this section, we assume that the function ψ : ℝ+5® ℝ+satisfies the followingconditions:(C1) ψ is a strictly increasing, continuous function in each coordinate, and(C2) ... x0)).By the condition (3), {n(d(x0, x1))}nÎNis decreasing, it must converges to some h ≥0. We claim that h = 0. On the contrary, assume that h > 0. Then, by the definition of the ... ℝ+is a continuous function such that ψ(x, y)=0if and only if x = y =0. In [6,7], the authors proved some fixed point results for the C-contractions. In thissection, we present some fixed point...