"Aspects and Applications of p-Integer-Based Meyer-König-Zeller Durrmeyer Operators"

Within this paper, our study presents a novel class of Meyer-König-Zeller Durrmeyer (MKZD) type operators integrated with the concept of ppp-integers, which adds a new dimension to the approximation process in the context of positive linear operators. The introduction of ppp-integers in the construction of MKZD operators allows greater flexibility and adaptability in handling different functional behaviors, particularly in scenarios requiring finer approximation properties. This generalization opens up new avenues for theoretical development and practical applications in numerical analysis and approximation theory. We rigorously define the newly constructed operators and investigate their basic properties, including linearity, positivity, and preservation of certain test functions. The core objective of this work is to analyze the rate of convergence of these ppp-MKZD operators, especially in terms of the modulus of continuity and Peetre’s K-functional. Emphasis is placed on the confluence behavior of the operators — that is, how effectively they approximate continuous functions as the parameters approach their limiting values. We derive upper bounds for the approximation error and support our theoretical results with illustrative examples. Additionally, the study highlights how the involvement of ppp-integers enhances the convergence behavior of the operators under various function spaces, thereby demonstrating their applicability in solving practical problems in computational mathematics. This work not only deepens the understanding of MKZD-type operators but also offers a foundation for future investigations into more generalized operator forms and their applications. The proposed operators could be particularly useful in approximation scenarios involving functions with varying smoothness and bounded variation.