Approximation by Quantum Meyer-König-Zeller Fractal Functions

In this paper, a novel class of quantum fractal functions is introduced based on the Meyer-König-Zeller operator (Formula presented.). These quantum Meyer-König-Zeller (MKZ) fractal functions employ (Formula presented.) as the base function in the iterated function system for (Formula presented.) -fractal functions. For (Formula presented.), I closed interval in (Formula presented.), it is shown that a sequence of quantum MKZ fractal functions (Formula presented.) exists which converges uniformly to f without altering the scaling function (Formula presented.). The shape of (Formula presented.) depends on q as well as the other iterated function system parameters. For (Formula presented.), (Formula presented.), we show that a sequence (Formula presented.) exists with (Formula presented.) converging to f. Quantum MKZ fractal versions of some classical Müntz theorems are also presented. For (Formula presented.), the box dimension and some approximation-theoretic results of MKZ (Formula presented.) -fractal functions are investigated in (Formula presented.). Finally, MKZ (Formula presented.) -fractal functions are studied in (Formula presented.) spaces with (Formula presented.).