Weighted Korovkin-Type Theorem and Some Properties of Szász–Mirakjan Operators Preserving Exponential Functions via Power Series Statistical Convergence

In this article, we establish a weighted Korovkin-type approximation theorem within the framework of power series statistical convergence and provide a systematic extension of classical Korovkin theory to weighted function spaces. Furthermore, we investigate the approximation properties of the Szász–Mirakjan operators preserving exponential functions. In addition, we derive quantitative estimates for the rate of convergence by using appropriate modulus of continuity. Our results show that the proposed weighted Korovkin-type theorem remains applicable even in situations where the classical Korovkin framework does not ensure convergence, highlighting the effectiveness of power series statistical convergence in overcoming the limitations of classical methods. Finally, several illustrative examples and graphs are provided to demonstrate the accuracy and efficiency of the operators and to support the theoretical findings. MSC2020 Classification: 41A36 and 40C15.