The aim of this paper is to present a Stancu type Kantorovich modification of q−BernsteinSchurer operators introduced by Muraru [22] and modified by Ren and Zeng [29]. Here, we obtain a convergence theorem by using the well known Bohman-Korovkin criterion and find the estimate of the rate of convergence by means of modulus of continuity and Lipschitz function for these operators. Also, we estab...

In this paper we introduce the Bézier variant of genuine-Durrmeyer type operators having Pólya basis functions. We give a global approximation theorem in terms of second order modulus of continuity, a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem by using the Ditzian-Totik modulus of smoothness. The rate of convergence for funct...

Let N be a set of positive integers and let F(z) = I Anz" be an entire function for which An0 (n 0 N). It is reasonable to expect that, if D denotes the density of the set N in some sense, then F(z) will behave somewhat similarly in every angle of opening greater than 2vD. For functions of finite order, the appropriate density seems to be the P6lya maximum density 9. In this paper we introduce ...

Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variati01~al analysis and its applications, especially for issues related to variational stability and optimizatiou. \Ve develop an approach to variational stability based on generalized differentiation. The principal achievements of this paper include new results on coderivative ...

A new class of regular quaternionic functions, defined by power series in a natural fashion, has been introduced in [11]. Several results of the theory recall the classical complex analysis, whereas other results reflect the peculiarity of the quaternionic structure. The recent [1] identified a larger class of domains, on which the study of regular functions is most natural and not limited to t...

This paper presents introduce some new notions, f -asymptotically equivalent of multiple L, strong f -asymptotically equivalent of multiple L, and strong f -asymptotically lacunary equivalent of multiple L which is a natural combination of the definition for asymptotically equivalent, Statistically limit, Lacunary sequence, and Modulus function. We study some connections between the asymptotica...

This paper presents a new method of model selection for regression problems using the modulus of continuity. For this purpose, we suggest the prediction risk bounds of regression models using the modulus of continuity which can be interpreted as the complexity of functions. We also present the model selection criterion referred to as the modulus of continuity information criterion (MCIC) which ...

Abstract. We consider the equation −∆u = wf (u) on a symmetric bounded domain in Rn with Dirichlet boundary conditions. Here w is a positive function or measure that is invariant under the (Euclidean) symmetries of the domain. We focus on solutions u that are positive and/or have a low Morse index. Our results are concerned with the existence of non-symmetric solutions and the non-existence of ...

Iterative constant modulus algorithms have been used to blindly separate and retrieve interfering constant modulus signals impinging on an antenna array. These algorithms have several well-known but basically unsolved deficiencies. In this paper, we present an algorithm to analytically compute the solution to the underlying constant modulus (CM) factorization problem. With this new approach, it...