Browsing by Author "Rao, Nadeem"

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A Note on a General Sequence of Λ -Szasz Kantorovich Type Operators
(Springer Heidelberg, 2024) Rao, Nadeem; Ayman-Mursaleen, Mohammad; Aslan, Resat
In the present manuscript, we study the approximation properties of modified Sz & aacute;sz Kantorovich operators with a new modification of blending type which depends on parameters, lambda is an element of [-1, 1] and rho > 0. Further, we prove a Korovkin-type approximation theorem and obtain the rate of convergence of these operators. Next, their graphical depiction, error analysis and convergence behaviour of these operators for the different functional spaces are discussed. Moreover, univariate and bivariate version of these sequences of operators are introduced in their respective blocks. Rate of convergence, order of approximation, local approximation, global approximation in terms of weight function and A-statistical approximation results are investigated via first and second-order modulus of smoothness, Lipschitz classes, Peetre's K-functional in different spaces of functions.
On a Novel Class of (Λ, Ν)-Bernstein Operators: Approximation Results on Bogel Spaces and Associated Graphical Error Estimates
(Springer Heidelberg, 2025) Ozger, Zeynep Odemis; Bansal, Shivani; Aslan, Resat; Rao, Nadeem
In this paper, we consider a novel sequence of modified bivariate Bernstein-Stancu operators and investigate some precious approximation properties of proposed operators. With the aid of two-dimensional test functions and central moments, we derive essential estimates to establish uniform convergence and determine the order of approximation. Additionally, we present local approximation results in the context of Lipschitz maximal functions. Furthermore, we explore the applicability of these operators in Bogel spaces and employ the mixed modulus of continuity to evaluate their performance. To validate our theoretical results, we perform numerical experiments that illustrate the precision, effectiveness and advantages of the proposed approach in practical applications of the proposed operators.