scholarly journals On New Classes of Stancu-Kantorovich-Type Operators

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1235
Author(s):  
Bianca Ioana Vasian ◽  
Ștefan Lucian Garoiu ◽  
Cristina Maria Păcurar
Keyword(s):  
Test Functions ◽  
New Class ◽  
Convergence Results ◽  
Error Estimations ◽  
Kantorovich Operators

The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e0(x)=1 and e1(x)=x, e0(x)=1 and e2(x)=x2, as well as e1(x)=x and e2(x)=x2. The class of operators that preserve the test functions e1(x)=x and e2(x)=x2 is a genuine generalization of the class introduced by Indrea et al. in their paper “A New Class of Kantorovich-Type Operators”, published in Constr. Math. Anal.

Existence and convergence for a new multivalued hybrid mapping in CAT(κ) spaces

2017 ◽  
Vol 33 (3) ◽  
pp. 319-326
Author(s):  
EMIRHAN HACIOGLU ◽  
◽  
VATAN KARAKAYA ◽  
Keyword(s):  
Hilbert Spaces ◽  
Multivalued Mappings ◽  
Hybrid Mapping ◽  
New Class ◽  
Convergence Results

Most of the studies about hybrid mappings are carried out for single-valued mappings in Hilbert spaces. We define a new class of multivalued mappings in CAT (k) spaces which contains the multivalued generalization of (α, β) - hybrid mappings defined on Hilbert spaces. In this paper, we prove existence and convergence results for a new class of multivalued hybrid mappings on CAT(κ) spaces which are more general than Hilbert spaces and CAT(0) spaces.

scholarly journals Completely generalized multivalued nonlinear quasi-variational inclusions

2002 ◽  
Vol 30 (10) ◽  
pp. 593-604 ◽  
Author(s):  
Zeqing Liu ◽  
Lokenath Debnath ◽  
Shin Min Kang ◽  
Jeong Sheok Ume
Keyword(s):  
Existence Theorems ◽  
Maximal Monotone ◽  
Iterative Algorithms ◽  
Monotone Mappings ◽  
Operator Technique ◽  
Variational Inclusions ◽  
New Class ◽  
Convergence Results ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator

We introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou-Yao, Kazmi, Noor, Noor-Al-Said, Noor-Noor, Noor-Noor-Rassias, Shim-Kang-Huang-Cho, Siddiqi-Ansari, Verma, Yao, and Zhang.

scholarly journals On Generalized Nonexpansive Maps in Banach Spaces

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 61 ◽  
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel de la Sen
Keyword(s):  
Banach Spaces ◽  
General Class ◽  
Iterative Algorithms ◽  
Uniformly Convex ◽  
Demiclosed Principle ◽  
New Class ◽  
Nonexpansive Maps ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces ◽  
Expansive Maps

We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized α -non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms.

scholarly journals On weak and strong convergence of an explicit iteration process for a total asymptotically quasi-I-nonexpansive mapping in Banach space

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1699-1710
Author(s):  
Hukmi Kiziltunc ◽  
Yunus Purtas
Keyword(s):  
Banach Space ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Iterative Process ◽  
Iteration Process ◽  
Nonempty Closed Convex Subset ◽  
Weak And Strong Convergence ◽  
New Class ◽  
Convergence Results ◽  
Definition Of

In this paper, we introduce a new class of Lipschitzian maps and prove some weak and strong convergence results for explicit iterative process using a more satisfactory definition of self mappings. Our results approximate common fixed point of a total asymptotically quasi-I-nonexpansive mapping T and a total asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.

scholarly journals Note on a Schurer-Stancu-type operator

2015 ◽  
Vol 24 (1) ◽  
pp. 61-67
Author(s):  
ADRIAN D. INDREA ◽  
◽  
ANAMARIA INDREA ◽  
PETRU I. BRAICA ◽  
◽  
...  
Keyword(s):  
Type Theorem ◽  
Type Operator ◽  
Test Functions ◽  
New Class ◽  
Voronovskaja Type Theorem

The aim of this paper is to introduce a class of operators of Schurer-Stancu-type with the property that the test functions e0 and e1 are reproduced. Also, in our approach, a theorem of error approximation and a Voronovskaja-type theorem for this operators are obtained. Finally, we study the convergence of the iterates for our new class of operators.

A new elliptic mixed boundary value problem with (p,q)-Laplacian and Clarke subdifferential: Existence, comparison and convergence results

2021 ◽  
pp. 1-20
Author(s):  
Shengda Zeng ◽  
Stanisław Migórski ◽  
Domingo A. Tarzia
Keyword(s):  
Boundary Value Problem ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Partial Differential Operator ◽  
Convergence Result ◽  
Generalized Gradient ◽  
New Class ◽  
Convergence Results ◽  
Surjectivity Result ◽  
Dependence Result

The goal of this paper is to investigate a new class of elliptic mixed boundary value problems involving a nonlinear and nonhomogeneous partial differential operator [Formula: see text]-Laplacian, and a multivalued term represented by Clarke’s generalized gradient. First, we apply a surjectivity result for multivalued pseudomonotone operators to examine the existence of weak solutions under mild hypotheses. Then, a comparison theorem is delivered, and a convergence result, which reveals the asymptotic behavior of solution when the parameter (heat transfer coefficient) tends to infinity, is obtained. Finally, we establish a continuous dependence result of solution to the boundary value problem on the data.

A NEW CLASS OF FRACTAL INTERPOLATION SURFACES BASED ON FUNCTIONAL VALUES

Fractals ◽  
2016 ◽  
Vol 24 (01) ◽  
pp. 1650007 ◽  
Author(s):  
A. K. B. CHAND ◽  
N. VIJENDER
Keyword(s):  
Iterated Function Systems ◽  
Fractal Interpolation ◽  
Shape Parameters ◽  
Positive Real ◽  
Scaling Factors ◽  
Numerical Illustration ◽  
New Class ◽  
Convergence Results ◽  
Iterated Function

Fractal interpolation is a modern technique for fitting of smooth/non-smooth data. Based on only functional values, we develop two types of [Formula: see text]-rational fractal interpolation surfaces (FISs) on a rectangular grid in the present paper that contain scaling factors in both directions and two types of positive real parameters which are referred as shape parameters. The graphs of these [Formula: see text]-rational FISs are the attractors of suitable rational iterated function systems (IFSs) in [Formula: see text] which use a collection of rational IFSs in the [Formula: see text]-direction and [Formula: see text]-direction and hence these FISs are self-referential in nature. Using upper bounds of the interpolation error of the [Formula: see text]-direction and [Formula: see text]-direction fractal interpolants along the grid lines, we study the convergence results of [Formula: see text]-rational FISs toward the original function. A numerical illustration is provided to explain the visual quality of our rational FISs. An extra feature of these fractal surface schemes is that it allows subsequent interactive alteration of the shape of the surfaces by changing the scaling factors and shape parameters.

scholarly journals Chebyshev-Fourier Spectral Methods for Nonperiodic Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Bojan Orel ◽  
Andrej Perne
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Spectral Methods ◽  
Boundary Value ◽  
Absolute Error ◽  
Method Error ◽  
Linear Ordinary Differential Equations ◽  
New Class ◽  
Convergence Results ◽  
The Given

A new class of spectral methods for solving two-point boundary value problems for linear ordinary differential equations is presented in the paper. Although these methods are based on trigonometric functions, they can be used for solving periodic as well as nonperiodic problems. Instead of using basis functions periodic on a given interval−1,1, we use functions periodic on a wider interval. The numerical solution of the given problem is sought in terms of the half-range Chebyshev-Fourier (HCF) series, a reorganization of the classical Fourier series using half-range Chebyshev polynomials of the first and second kind which were first introduced by Huybrechs (2010) and further analyzed by Orel and Perne (2012). The numerical solution is constructed as a HCF series via differentiation and multiplication matrices. Moreover, the construction of the method, error analysis, convergence results, and some numerical examples are presented in the paper. The decay of the maximal absolute error according to the truncation numberNfor the new class of Chebyshev-Fourier-collocation (CFC) methods is compared to the decay of the error for the standard class of Chebyshev-collocation (CC) methods.

A new class of test functions for global optimization

2006 ◽  
Vol 38 (3) ◽  
pp. 479-501 ◽  
Author(s):  
Bernardetta Addis ◽  
Marco Locatelli
Keyword(s):  
Global Optimization ◽  
Test Functions ◽  
New Class
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