In this paper we discuss the issue of solving stochastic optimization problems by means of sample average approximations. Our focus is on rates of convergence of estimators of optimal solutions and optimal values with respect to the sample size. This is a well studied problem in case the samples are independent and identically distributed (i.e., when standard Monte Carlo is used); here, we stud...

In this paper we discuss the issue of solving stochastic optimization problems by means of sample average approximations. Our focus is on rates of convergence of estimators of optimal solutions and optimal values with respect to the sample size. This is a well-studied problem in case the samples are independent and identically distributed (i.e., when standard Monte Carlo simulation is used); he...

In this paper, we introduce a parametric extension of certain family summation-integral type operators on the interval [0,∞). Firstly, obtain test functions and central moments. Secondly, investigate weighted approximation properties for these estimate rate convergence. Then, give pointwise Peetre K-functional Lipschitz class. Moreover, demonstrate Voronovskaja theorem operators. Finally, conve...

We consider trigonometric interpolations with shifted equidistant nodes and investigate their accuracies depending on the shift parameter. Two different types of interpolations are in the focus of our attention: the Krylov-Lanczos and the rational-trigonometric-polynomial interpolations. In both cases, we find optimal shifts that provide with the best accuracy in different frameworks.

The note contains two examples of function spaces Cp(X) endowed with the pointwise topology. The first example is Cp(M),M being a planar continuum, such that Cp(M) is uniformly homeomorphic to Cp(M) if and only ifm = n. This strengthens earlier results concerning linear homeomorphisms. The second example is a non-Lindelöf function space Cp(X), whereX is a monolithic perfectly normal compact spa...

In this paper, we prove the existence of a random fixed point of by using pointwise asymptotically nonexpansive random operator and the stability resultsof two iterative schemes for random operator.

Various Bayesian wavelet estimators have been proposed recently in literature. Following Bayesian approach, a prior distribution is imposed on wavelet coefficients of the unknown response function and a Bayesian estimator is obtained then by applying a suitable Bayesian rule to the resulting posterior distribution of the coefficients. Numerous simulations studies demonstrate the good performanc...

In numerical analysis it is important to construct interpolating polynomials approximating a given function and its derivatives simultaneously. The authors define some new good interpolating matrices with "many" nodes close to the endpoints of the interval and also give error estimates.

We are motivated by applications that need rich model classes to represent the application, such as the set of all discrete distributions over large, countably infinite supports. But such rich classes may be too complex to admit estimators that converge to the truth with convergence rates that can be uniformly bounded over the entire model class as the sample size increases (uniform consistency...