Type Convergence Theorem Research Articles

Some Approximation Results on $\lambda-$ Szasz-Mirakjan-Kantorovich Operators

In this article, we purpose to obtain several approximation properties of Sz\'{a}sz-Mirakjan-Kantorovich operators with shape parameter $\lambda \in\lbrack-1,1]$. We compute some preliminaries results such as moments and central moments for these operators. Next, we derive the Korovkin type convergence theorem, estimate the degree of convergence with respect to the moduli of continuity, for the functions belong to Lipschitz-type class and Peetre's $K$-functional, respectively. Further, we investigate Voronovskaya type asymptotic theorem and give the comparison of the convergence of these newly defined operators to the certain functions with some graphics.

A New Class of Kantorovich-Type Operators

The purpose of the paper called “A new class of Kantorovich-type operators”, as the title says, is to introduce a new class of Kantorovich-type operators with the property that the test functions $e_1$ and $e_2$ are reproduced. Furthermore, in our approach, an asymptotic type convergence theorem, a Voronovskaja type theorem and two error approximation theorems are given. As a conclusion, we make a comparison between the classical Kantorovich operators and the new class of Kantorovich - type operators.

Convergence results in Birkhoff weak integrability

This article presents some properties of real Birkhoff weak integrable functions with respect to a non-additive set function, such as H??lder inequality, Minkowski inequality, Lebesgue type convergence theorems and Fatou type theorem.

An Hélein’s type convergence theorem for conformal immersions from 𝕊² to manifold

In this short paper, we establish an Hélein’s type convergence theorem for conformal immersions from S 2 \mathbb {S}^{2} to a general compact Riemannian manifold. As an application, we extend the existence of minimizer of ∫ | A | 2 d μ \int |A|^{2} d\mu for immersed 2-spheres in compact 3-manifolds under certain conditions due to E. Kuwert, A. Mondino, and J. Schygulla to higher codimensions.

Strong convergence properties for partial sums of asymptotically negatively associated random vectors in Hilbert spaces

In this paper, we investigate the almost sure convergence for partial sums of asymptotically negatively associated (ANA, for short) random vectors in Hilbert spaces. The Khintchine-Kolmogorov type convergence theorem, three series theorem and the Kolmogorov type strong law of large numbers for partial sums of ANA random vectors in Hilbert spaces are obtained. The results obtained in the paper generalize some corresponding ones for independent random vectors and negatively associated random vectors in Hilbert spaces.

Some properties and convergence theorems for fuzzy-valued Kluvánek–Lewis integrals

In this paper, we first introduce a new fuzzy-valued integral of scalar-valued functions with respect to a fuzzy-valued measure with some natural properties. Then we prove Vitali type convergence theorem and dominated convergence theorem for this kind of integral.

A new fuzzy-valued integral and its convergence theorems

In this paper, we generalize Kluv?anek-Lewis type set-valued integral to fuzzy number measures in Banach spaces. Firstly, we introduce the new fuzzy-valued integral with some natural properties. And then, We establish Vitali type convergence theorem and dominated convergence theorem for this kind of integral.

On nonlinear bivariate singular integral operators

In this paper, we give some pointwise convergence and Fatou type convergence theorems for a family of nonlinear bivariate singular integral operators in the following form: urn:x-wiley:mma:media:mma5425:mma5425-math-0006 where m1,m2 ≥ 1 are fixed natural numbers, and ω ∈ Ω, Ω denotes a nonempty set of indices endowed with a topology. Here, denotes a family of kernel functions and f belongs to the space of Lebesgue integrable functions . Some numerical examples and graphical illustrations supporting the results are also given.

Strict and Mackey topologies and tight vector measures

Let B() denote the Banach algebra of all bounded Borel measurable complex functions defined on a topological Hausdorff space X, and Bo() stand for the ideal of B() consisting of all functions vanishing at infinity. Then B() is a faithful Banach left Bo()-module and the strict topology β on B() induced by Bo() is a mixed topology. For a sequentially complete locally convex Hausdorff space (E, ξ), we study the relationship between vector measures m : → E and the corresponding continuous integration operators Tm : B() → E. It is shown that a measure m : → E is countably additive tight if and only if the corresponding integration operator Tm is (η, ξ)-continuous, where η denotes the infimum of the strict topology β and the Mackey topology τ (B(), ca()). If, in particular, E is a Banach space, it is shown that m is countably additive tight if and only if Tm(absconv(U ∪ W)) is relatively weakly compact in E for some τ (B(), ca())-neighborhood U of 0 and some β-neighborhood W of 0 in B(). As an application, we prove a Nikodym type convergence theorem for countably additive tight vector measures.

Viscosity approximations methods for ( ψ , φ ) $(\psi,\varphi)$ -weakly contractive mappings

In this paper, we study viscosity approximations with $(\psi,\varphi)$ -weakly contractive mappings. We show that Moudafi’s viscosity approximations follow from Browder and Halpern type convergence theorems. Our results generalize a number of convergence theorems including a strong convergence theorem of Song and Liu (Fixed Point Theory Appl. 2009:824374, 2009).

Nonexpansive semigroups in CAT ( κ ) spaces

The main purpose of this paper is to study Browder type convergence theorems for a nonexpansive semigroup with geometric approaches in a CAT(κ) space. Besides, we determine a necessary and sufficient condition for convergence of a Browder type iteration associated to a uniformly asymptotically regular nonexpansive semigroup on the unit sphere in an infinite-dimensional Hilbert space. MSC:47H20, 47H10.

Third order convergence theorem for a family of Newton like methods in Banach space

In this paper, we propose a family of Newton-like methods in Banach space which includes some well known third-order methods as particular cases. We establish the Newton-Kantorovich type convergence theorem for a proposed family and get an error estimate.

Newton-Kantorovich and Smale Uniform Type Convergence Theorem for a Deformed Newton Method in Banach Spaces

Newton-Kantorovich and Smale uniform type of convergence theorem of a deformed Newton method having the third-order convergence is established in a Banach space for solving nonlinear equations. The error estimate is determined to demonstrate the efficiency of our approach. The obtained results are illustrated with three examples.

Rainwater–Simons type convergence theorems for generalized convergence methods

We extend the well-known Rainwater–Simons convergence theorem to various generalized convergence methods such as strong matrix summability, statistical convergence and almost convergence. In fact we prove these theorems not only for boundaries but for the more general notion of (I)-generating sets introduced by Fonf and Lindenstrauss.

On the Convergence and Well-Balanced Property of Path-Conservative Numerical Schemes for Systems of Balance Laws

This paper deals with the numerical approximation of one-dimensional hyperbolic systems of balance laws. We consider these systems as a particular case of hyperbolic systems in nonconservative form, for which we use the theory introduced by Dal Maso, LeFloch and Murat (J. Math. Pures Appl. 74:483, 1995) in order to define the concept of weak solutions. This theory is based on the prescription of a family of paths in the phases space. We also consider path-conservative schemes, that were introduced in Pares (SIAM J. Numer. Anal. 44:300, 2006). The first goal is to prove a Lax-Wendroff type convergence theorem. In Castro et al. (J. Comput. Phys. 227:8107, 2008) it was shown that, for general nonconservative systems a rather strong convergence assumption is needed to prove such a result. Here, we prove that the same hypotheses used in the classical Lax-Wendroff theorem are enough to ensure the convergence in the particular case of systems of balance laws, as the numerical results shown in Castro et al. (J. Comput. Phys. 227:8107, 2008) seemed to suggest. Next, we study the relationship between the well-balanced properties of path-conservative schemes applied to systems of balance laws and the family of paths.

On Brooks–Jewett, Vitali–Hahn–Saks and Nikodým convergence theorems for quasi-triangular functions

Connections are established between Brooks–Jewett, Vitali–Hahn–Saks and Nikodym type convergence theorems for quasi-triangular functions on Boolean rings satisfying the Subsequential Completeness Property and valued into Hausdorff topological spaces.

Convergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems

AbstractWe discuss the following viscosity approximations with the weak contraction "Equation missing" for a non-expansive mapping sequence "Equation missing", "Equation missing", "Equation missing". We prove that Browder's and Halpern's type convergence theorems imply Moudafi's viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern's type iteration and Mouda's viscosity approximations with the weak contraction.

Newton–Kantorovich type convergence theorem for a family of new deformed Chebyshev method

In this paper, a family of new deformed Chebyshev method with third-order is proposed in Banach space which is used to solve the nonlinear operator equations. The Newton–Kantorovich convergence theorem for the family of new deformed Chebyshev method is established by using majorizing function. The error estimate is also obtained. Finally, few examples are provided to show the application of our theorems.

Browder’s type convergence theorems for one-parameter semigroups of nonexpansive mappings in Banach spaces

In this paper, we prove Browder’s type convergence theorems for one-parameter strongly continuous semigroups of nonexpansive mappings in Banach spaces.

Moudafi's viscosity approximations with Meir–Keeler contractions

In this paper, we discuss Moudafi's viscosity approximations with Meir–Keeler contractions. We first present very simple proofs of Xu's theorems concerning Moudafi's approximations. We next prove that Browder's and Halpern's type convergence theorems imply Moudafi's viscosity approximations. Using them, we finally state several deduced theorems.