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The goal of this manuscript is to introduce a new sequence of generalized-Baskakov-Durrmeyer-Schurer Operators. Further, basic estimates are calculated. In the subsection sequence, rapidity of convergence and order of approximation are studied in terms of first and second order modulus of continuity. We prove a Korovkin-type approximation theorem and obtain the rate of convergence of these operators. Moreover, local and global approximation properties are discussed in different functional spaces. Lastly, A-statistical approximation results are presented. [ABSTRACT FROM AUTHOR]

This research article presents modified Szász-Mirakjan operators that fix exponential spaces. We derive moments and central moments, convergence rate and approximation results of the operators in weighted exponential spaces. The graphical analysis shows that our operator gives better results with exponential functions. [ABSTRACT FROM AUTHOR]

In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

The key goal of the present research article is to introduce a new sequence of linear positive operator i.e., α-Schurer Durrmeyer operator and their approximation behaviour on the basis of function η(z), where η infinitely differentiable on [0, 1], η(z) = 0, η(1) = 1 and η'(z) > 0, for all z ∈ [0, 1]. Further, we calculate central moments and basic estimates for the sequence of the operators. Moreover, we discuss the rate of convergence and order of approximation in terms of modulus of continuity, smoothness, Korovkin theorem and Peeter's K-functional. In the subsequent sections local, global and A-Statistical result are studied. [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]

In this paper, we define Bézier variant of generalized Bernstein-Durrmeyer type operators of second order, introduced by Ana et al. Then, we find error estimate in terms of terms of Ditzian Totik modulus of smoothness. Next, we study rate of approximation for larger class function of bounded variation. [ABSTRACT FROM AUTHOR]

The optimal order of approximation, |Ln f(x) − f(x)| of a linear positive operator Ln f(x) is 1/n and can not be improved however smooth the function may be. We remove the positivity of the Baskakov operator Vn(f ;x) and introduce its three variants VnM,i (f ;x), i = 1,2,3. We prove that the rates of approximation by these operators are improved from the linear order 1/n to quadratic order 1/n² and then to cubic order 1/n³ for sufficiently smooth functions. [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]

This paper deals with the approximation properties of a generalized version of Szász–Mirakjan operators which preserve a x {a^{x}} , a > 1 {a>1} (fixed), and x ≥ 0 {x\geq 0}. The uniform convergence of the operators is studied by using some auxiliary results. Also, error estimations are determined by considering the functions from different spaces. The convergence of the said operators is shown and analyzed by graphics. In the same direction, the proposed operators are compared with Szász–Mirakjan operators for the rate of convergence. A Voronovskaya-type theorem is considered and a comparison with Szász–Mirakjan operators is shown in the sense of convexity. To describe the quantitative means of an asymptotic formula, we quantitatively approach the Voronovskaya-type theorem; moreover, a Grüss–Voronovskaya-type theorem is proved. For further investigations regarding the approximation for functions from various spaces, two significant extensions are added keeping in mind some developments in the L p {L_{p}} -space. One is the Kantorovich variant and the other one is the Durrmeyer modification of the defined operators. Here, the rate of convergence is described by means of the function with a derivative of bounded variation for the Durrmeyer modified operators for which some properties are discussed. Also, A-statistical properties of the Durrmeyer modified operators are established. This paper ends by presenting some significant statements and the conclusion. [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]

In this paper, bivariate Sádsz-Mirakjan type operators are introduced along with the estimation of its approximation properties and its rate of convergence. Furthermore, to check the asymptotic behavior of the said bivariate operators, Voronovskaya type theorem is proved and determined the simultaneous approximation of the operators for first order partial derivative. Finally, the convergence behavior of the bivariate operators are obtained through graphical representation and validated the numerical results with the results of Sádsz-Mirakjan operators for the function of two variables. [ABSTRACT FROM AUTHOR]

In this paper, we study the approximation properties of bivariate summation‐integral–type operators with two parameters m,n∈N. The present work deals within the polynomial weight space. The rate of convergence is obtained while the function belonging to the set of all continuous and bounded function defined on ([0],∞)(×[0],∞) and function belonging to the polynomial weight space with two parameters, also convergence properties, are studied. To know the asymptotic behavior of the proposed bivariate operators, we prove the Voronovskaya type theorem and show the graphical representation for the convergence of the bivariate operators, which is illustrated by graphics using Mathematica. Also with the help of Mathematica, we discuss the comparison by means of the convergence of the proposed bivariate summation‐integral–type operators and Szász‐Mirakjan‐Kantorovich operators for function of two variables with two parameters to the function. In the same direction, we compute the absolute numerical error for the bivariate operators by using Mathematica and is illustrated by tables and also the comparison takes place of the proposed bivariate operators with the bivariate Szász‐Mirakjan operators in the sense of absolute error, which is represented by table. At last, we study the simultaneous approximation for the first‐order partial derivative of the function. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain local approximation results for Stancu type generalization of modified Szász-Mirakjan operators. First, we calculate moments of the operators. Some direct results of the operators are investigated. The rate of convergence of the operators is evaluated. In last section of the paper, the Voronovskaya type result is obtained. [ABSTRACT FROM AUTHOR]

In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators. [ABSTRACT FROM AUTHOR]

In this paper, we investigate Stancu variant of generalized (p; q)-Szász-Mirakyan operators. Initially, we estimate moments of the operators. Using Korovkin’s result, we have evaluated the uniform convergence of the operators. Direct results of the operators have been appraised. For better approximation we have calculated the rate of convergence of the operators. Last, we have proved Voronovskaya type theorem for the operators. Particularly, if α = 0 then we get the generalized (p; q)-Szász-Mirakyan operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Stancu type generalization of modified Srivastava-Gupta operators. We obtain the moments of the operators and then prove the basic convergence theorem. Next, the Voronovskaja type asymptotic formula and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then, we obtain point-wise estimates using the Lipschitz type maximal function and two parameter Lipschitz-type space. Further, we study the A-statistical convergence of these operators. Lastly, we give better estimations of the above operators using King type approach. [ABSTRACT FROM AUTHOR]

In this paper, a kind of modified Baskakov–Schurer–Szász operators (1.2) is introduced. Approximation properties of theses operators are explored: the rate of convergence in terms of the usual moduli of smoothness is given, the convergence in certain weighted spaces is investigated. Furthermore, we study q -analogues of Baskakov–Schurer–Szász operators and its Stancu generalization. Then the better error estimations for the operators (6.3) by using King type approach is investigated. In the last section the Korovkin type weighted statistical approximation property of operators (9.1) is given. [ABSTRACT FROM AUTHOR]

We introduce certain modified Szász-Mirakyan operators in polynomial weighted spaces of functions of one variable. We studied approximation properties of these operators. [ABSTRACT FROM AUTHOR]

In the present paper we propose the Durrmeyer-Baskakov-Stancu operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0,∞). Also, Voronovskaja type theorem is studied. [ABSTRACT FROM AUTHOR]

We obtain global rates of approximation by qq-Durrmeyer operators Dn,q(f;x) for the functions in the class Lp([0,1]), 1 ≤ p ≤ ∞. First, rates of approximation in terms of the norms of f and f' and in terms of the ordinary modulus of smoothness are obtained. Subsequently, we obtain rates of approximation in terms of the generalized modulus of smoothness ωφ(f,δ). [ABSTRACT FROM AUTHOR]