Search

In this paper we give direct approximation theorems and the Voronovskaya type asymptotic formula for certain linear operators associated with the Hermite polynomials. These operators extend the well-known Szász-Mirakjan operators. [ABSTRACT FROM AUTHOR]

In this paper, a Dunkl type generalization of Stancu type q-Szász-Mirakjan-Kantorovich positive linear operators of the exponential function is introduced. With the help of well-known Korovkin's theorem, some approximation properties and also the rate of convergence for these operators in terms of the classical and second-order modulus of continuity, Peetre's K-functional and Lipschitz functions are investigated. [ABSTRACT FROM AUTHOR]

The split feasibility problem (SFP) has many applications, which can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator's range. In this paper, we introduce a new projection method to solve the SFP and prove its convergence under standard assumptions. Our results improve previously known corresponding methods and results of this area. The preliminary numerical experiments illustrates the advantage of our proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we solve Cauchy problem for a general form of an inhomogeneous Euler-Poisson-Darboux equation, where Bessel operator acts instead of the each second derivative. In the classical formulation, the Cauchy problem for this equation is not correct. However, for a specially selected form of the initial conditions, the equation has a solution. The general form of the Euler-Poisson-Darboux equation with such conditions we will call the singular Cauchy problem. [ABSTRACT FROM AUTHOR]

Let Ω ⊂ ℝp, p ∈ ℕ* be a nonempty subset and B(Ω) be the Banach lattice of all bounded real functions on Ω, equipped with sup norm. Let X ⊂ B(Ω) be a linear sublattice of B(Ω) and A: X → X be a positive linear operator with constant functions as the fixed point set. In this paper, using the weakly Picard operators techniques, we study the iterates of the operator A: Some relevant examples are also given. [ABSTRACT FROM AUTHOR]

The paper deals with a class of linear positive operators expressed by q-series. By using modulus of smoothness an upper bound of approximation error is determined. We identify functions for which these operators provide uniform approximation over noncompact intervals. A particular case is delivered. [ABSTRACT FROM AUTHOR]

Consider a commutative diagram of bounded linear operators between Banach spaces ... with exact rows. In what ways are the spectral and local spectral properties of B related to those of the pairs of operators A and C? In this paper, we give our answers to this general question using tools from local spectral theory. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a split best proximity point and equilibrium problem, and find a solution of the best proximity point problem such that its image under a given bounded linear operator is a solution of the equilibrium problem. We construct an iterative algorithm to solve such problem in real Hilbert spaces and obtain a weak convergence theorem. Finally, we also give an example to illustrate our result. [ABSTRACT FROM AUTHOR]

The aim of our paper is to focus on some properties of hemi-slant submanifolds in metallic (and Golden) Riemannian manifolds. We give some characterizations of hemi-slant submanifolds in metallic or Golden Riemannian manifolds and we obtain integrability conditions for the distributions involved. Examples of hemi-slant submanifolds in metallic and Golden Riemannian manifolds are given. [ABSTRACT FROM AUTHOR]

Certain bounded linear operators T on a complex Hilbert space H which have 2-isometric liftings S on another space K ⊃ H are being investigated. We refer also to a more special type of liftings, as well as to those which additionally meet the condition S ∗SH ⊂ H. Furthermore we describe other types of dilations for T, which are close to 2-isometries. Among these we refer to expansive (concave) operators and also to Brownian unitary dilations. Different matrix representations for such operators are obtained, where matrix entries involve contractive operators. [ABSTRACT FROM AUTHOR]

In this paper we present two new alternative ways for the proof of Voronovskaja-type formula of the Bleimann, Butzer and Hahn bivariate operators, using the close connection between the recalled operators and Bernstein bivariate operators, respectively Stancu bivariate operators. [ABSTRACT FROM AUTHOR]

In this paper we study some approximation properties of a sequence of positive linear operators defined by means of the powered Baskakov basis. We prove that in the particular case of squared Baskakov basis the operators behave better than the classical Baskakov operators. For this particular case we give also a quantitative Voronovskaya type result. [ABSTRACT FROM AUTHOR]

In the present work, we discuss the existence of mild solutions for the initial value problem of fractional evolution equation of the form .... where CDtσ denotes the Caputo fractional derivative of order σ ∈ (0, 1), -A: D(A) ⊂ X → X generates a positive C0-semigroup T (t)(t ≥ 0) of uniformly bounded linear operator in X, b > 0 is a constant, f is a given functions. For this, we use the concept of measure of noncompactness in partially ordered Banach spaces whose positive cone K is normal, and establish some basic fixed point results under the said concepts. In addition, we relaxed the conditions of boundedness, closedness and convexity of the set at the expense that the operator is monotone and bounded. We also supply some new coupled fixed point results via MNC. To justify the result, we prove an illustrative example that rational of the abstract results for fractional parabolic equations. [ABSTRACT FROM AUTHOR]

In 2008 V. Miheşan constructed a general class of linear positive operators generalizing the Sźasz operators. In this article, a Durrmeyer variant of these operators is introduced which is a method to approximate the Lebesgue integrable functions. First, we derive some indispensable auxiliary results in the second section. We present a quantitative Voronovskaja type theorem, local approximation theorem by means of second order modulus of continuity and weighted approximation for these operators. The rate of convergence for differential functions whose derivatives are of bounded variation is also obtained. [ABSTRACT FROM AUTHOR]