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In the current paper a new form of Durrmeyer-type operator involving the beta function is introduced and its approximation properties are studied. We obtain the rate of convergence in different terms. Order of approximation for functions of some special class is also obtained. We establish the Voronovskaja type asymptotic result for this operator and the direct estimate. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a modification of Szfisz operators involving generalized Brenke type polynomials, First, we investigate Korovkin's type approximation theorem, Next, we established an approximation result for the functions in Lipschitz type space, Furthermore, we discuss the rate of convergence by means of the Ditzian-Totik modulus of smoothness, Lastly, we established an approximation result for the functions having derivatives of bounded variation. [ABSTRACT FROM AUTHOR]

The goal of the present manuscript is to introduce a new sequence of linear positive operators, i.e., Szász-Schurer-Beta type operators to approximate a class of Lebesgue integrable functions. Moreover, we calculate basic estimates and central moments for these sequences of operators. Further, rapidity of convergence and order of approximation are investigated in terms of Korovkin theorem and modulus of smoothess. In subsequent section, local and global approximation properties are studied in various functional spaces. [ABSTRACT FROM AUTHOR]

In the present paper, we consider Stancu-Jakimovski-Leviatan-Paltanea operators (SJLPoperators) involving Boas-Buck-Type polynomials. These polynomials include several important cases such as Brenke-type polynomials, Sheffer polynomials and Appell polynomials. We estimate the approximation properties of these operators using modulus of continuity, Peetre's K-functional and functions in Lipschitz type space. Moreover, we also prove some approximation results in the weighted spaces. Lastly, we discuss a Voronoskaja type theorem. [ABSTRACT FROM AUTHOR]

Runge's phenomenon reveals that interpolation methods lack uniform convergence of the sequence of the thus constructed polynomials to the function. The linear positive operators, however, can be relied on to ensure convergence across the whole domain. Further, linear positive operators can be modified suitably to approximate integrable functions. In this paper, we prove theoretical results on the estimates for the rate of approximation of a new sequence of operators. In addition, we find an error estimate for a larger class of functions, the functions of bounded variation. Finally, the theory is supported by suitable numerical examples, and the convergence estimates of the proposed operator are compared with the classical modified Bernstein–Durrmeyer operator. [ABSTRACT FROM AUTHOR]