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In the present paper, we construct a new sequence of Bernstein-Kantorovich operators depending on a parameter α. The uniform convergence of the operators and rate of convergence in local and global sense in terms of first- and second-order modulus of continuity are studied. Some graphs and numerical results presenting the advantages of our construction are obtained. The last section is devoted to bivariate generalization of Bernstein-Kantorovich operators and their approximation behaviors. [ABSTRACT FROM AUTHOR]

The study of infinite matrices is important in the theory of summability and in approximation. In particular, Toeplitz matrices or regular matrices and almost regular matrices have been very useful in this context. In this paper, we propose to use a more general matrix method to obtain necessary and sufficient conditions to sum the conjugate derived Fourier series. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a family of q-Szász-Mirakjan-Kantorovich type positive linear operators that are generated by Dunkl's generalization of the exponential function. We present approximation properties with the help of well-known Korovkin's theorem and determine the rate of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K-functional, and the second-order modulus of continuity. Furthermore, we obtain the approximation results for bivariate q-Szász-Mirakjan-Kantorovich type operators that are also generated by the aforementioned Dunkl generalization of the exponential function. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a new modification of Szász-Mirakyan operators based on $(p, q)$ -integers and investigate their approximation properties. We obtain weighted approximation and Voronovskaya-type theorem for new operators. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the Chlodowsky variant of $(p,q)$ Bernstein-Stancu-Schurer operators which is a generalization of $(p,q)$ Bernstein-Stancu-Schurer operators. We also discuss its Korovkin-type approximation properties and rate of convergence. [ABSTRACT FROM AUTHOR]

In this paper we introduce q-Szász-Mirakjan-Kantorovich operators generated by a Dunkl generalization of the exponential function and we propose two different modifications of the q-Szász-Mirakjan-Kantorovich operators which preserve some test functions. We obtain some approximation results with the help of the well-known Korovkin theorem and the weighted Korovkin theorem for these operators. Furthermore, we study convergence properties in terms of the modulus of continuity and the class of Lipschitz functions. This type of operator modification enables better error estimation than the classical ones. We also obtain a Voronovskaja-type theorem for these operators. [ABSTRACT FROM AUTHOR]

We propose a Kantorovich variant of (p,q)-analogue of Szász-Mirakjan operators. We establish the moments of the operators with the help of a recurrence relation that we have derived and then prove the basic convergence theorem. Next, the local approximation and weighted approximation properties of these new operators in terms of modulus of continuity are studied. [ABSTRACT FROM AUTHOR]

Kuhn-Tucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for constructing the best approximation to a reference point from the set of Kuhn-Tucker points of a general Hilbertian composite monotone inclusion problem. Applications to systems of coupled monotone inclusions are presented. Our framework does not impose additional assumptions on the operators present in the formulation, and it does not require knowledge of the norm of the linear operators involved in the compositions or the inversion of linear operators. [ABSTRACT FROM PUBLISHER]

The concepts of λ-equi-statistical convergence, λ-statistical pointwise convergence and λ-statistical uniform convergence for sequences of functions were introduced recently by Srivastava, Mursaleen and Khan [Math. Comput. Modelling, 55 (2012) 2040-2051.]. In this paper, we apply the notion of λ-equi-statistical convergence to prove a Korovkin type approximation theorem by using test functions 1, x/1+x, (x/1+x) ² and apply our result for the Bleimann, Butzer and Hahn [4] operators. We also study the rate of λ-equi-statistical convergence of a sequence of positive linear operators. [ABSTRACT FROM AUTHOR]

We introduce the notion of weighted A-statistical convergence of a sequence, where A represents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence. Further, we give a rate of weighted A-statistical convergence and apply the classical Bernstein polynomial to construct an illustrative example in support of our result. [ABSTRACT FROM AUTHOR]

In this work, we use the notion of (λ, μ)-statistical convergence to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions 1, x, y, x² + y². Furthermore, we define a new type of summability method via (λ, μ)-statistical convergence and use it to prove Korovkin theorem. Moreover, we obtain order of (λ, μ)-statistical convergence in our approximation. [ABSTRACT FROM AUTHOR]

In this paper, we prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical A-summability. We also construct an example by Meyer-König and Zeller operators to show that our result is stronger than those of previously proved by other authors. [ABSTRACT FROM AUTHOR]

We prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical summability (C, 1, 1). We also study the rate of statistical summability (C, 1, 1) of positive linear operators. Finally we construct an example to show that our result is stronger than those previously proved for Pringsheim's convergence and statistical convergence. [ABSTRACT FROM AUTHOR]

The concept Iu convergence was introduced by Baláz and Šalát [Uniform density u and corresponding Iu -convergence, Math. Comm., 11 (2006), 1-7]. Recently, Mursaleen and Edely [On the invariant mean and statistical convergence, Appl. Math. Letters, 22 (2009) 1700-1704] used the concept of invariant mean and density to study some new type of convergence methods. In this paper we generalize these two methods by using the concept of ideal convergence and invariant mean. Further we apply our method to prove a Korovkin type approximation theorem along with an example in support of our result. [ABSTRACT FROM AUTHOR]

In 1940 S. M. Ulam proposed at the University of Wisconsin the problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist". In 1982-2013, the second author solved the above Ulam problem for a variety of quadratic mappings. Interesting stability results have been achieved by S. A. Mohiuddine et al., since 2009. In this paper, we solve the Ulam stability problem for Euler-Lagrange (α, β; κ) quadratic mapping. The other authors of this research area have established important results also on functional inequalities. [ABSTRACT FROM AUTHOR]