Generating fractal functions associated with Suzuki iterated function systems

The paper’s Theorem 6 essentially proves that the Read–Bajraktarević operator T built from Lp and Fp has a unique fixed point under a Suzuki-type generalized φ-contraction hypothesis. The core inequality is shown in the paper by lifting the pointwise STGPC property of z ↦ Fp(y,z) to the function-space operator T via a sup-norm argument; however, there are substantive issues: (i) the STGPC condition for Fp is misstated in equation (10), comparing d(y, Fp(y,z)) to d(y,z) instead of the intended comparison in the second variable, namely d(z, Fp(y,z)) to d(z,t) (this is precisely the form needed in the proof) ; (ii) the definition of T in (12) is typeset incorrectly with a tuple instead of Fp(Lp^{-1}(y), h(Lp^{-1}(y))) ; and (iii) basic well-posedness details (T(C0(A)) ⊂ C0(A), continuity/gluing at partition points, and completeness of C0(A)) are not explicitly verified in the proof of Theorem 6, though they are standard consequences of the setup and the endpoint conditions (2) . The candidate model solution correctly supplies the missing completeness and endpoint-consistency checks and states the STGPC trigger in the correct second-variable form; however, it adds an unnecessary and flawed “Case B” subsequence argument for the STGPC lift (the simple sup-norm argument at a maximizer point suffices, as used implicitly in (13)–(15) of the paper) . The model also cites the wrong fixed-point reference (Suzuki 2009) for the φ-type generalized Suzuki condition actually used; the paper properly invokes a Pant (2018) theorem for STGPC fixed points . With these corrections, both approaches yield the same conclusion that T has a unique fixed point solving g(y) = Fp(Lp^{-1}(y), g(Lp^{-1}(y))).