Proofs of the Convergence Theorems

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

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A Class of Integral Operators that Fix Exponential Functions

Mediterranean Journal of Mathematics ◽

10.1007/s00009-021-01819-0 ◽

2021 ◽

Vol 18 (5) ◽

Author(s):

Carlo Bardaro ◽

Ilaria Mantellini ◽

Gumrah Uysal ◽

Basar Yilmaz

Keyword(s):

General Class ◽

Pointwise Convergence ◽

Type Theorem ◽

Integral Operators ◽

Exponential Functions ◽

Convergence Theorems ◽

Korovkin Type Theorem ◽

Type Formula

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

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A New Family of High-Order Ehrlich-Type Iterative Methods

Mathematics ◽

10.3390/math9161855 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1855 ◽

Cited By ~ 1

Author(s):

Petko D. Proinov ◽

Maria T. Vasileva

Keyword(s):

Iterative Methods ◽

Local Convergence ◽

Semilocal Convergence ◽

High Order ◽

Convergence Theorems ◽

New Family ◽

Special Cases ◽

Iteration Functions ◽

Iteration Function ◽

Local Convergence Analysis

One of the famous third-order iterative methods for finding simultaneously all the zeros of a polynomial was introduced by Ehrlich in 1967. In this paper, we construct a new family of high-order iterative methods as a combination of Ehrlich’s iteration function and an arbitrary iteration function. We call these methods Ehrlich’s methods with correction. The paper provides a detailed local convergence analysis of presented iterative methods for a large class of iteration functions. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with computer verifiable initial condition). As special cases of the main results, we study the convergence of several particular iterative methods. The paper ends with some experiments that show the applicability of our semilocal convergence theorems.

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Strong convergence theorems for finite families of pseudomonotone equilibrium and fixed point problems in Banach spaces

Afrika Matematika ◽

10.1007/s13370-020-00869-z ◽

2021 ◽

Author(s):

T. O. Alakoya ◽

L. O. Jolaoso ◽

O. T. Mewomo

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Banach Spaces ◽

Fixed Point Problems ◽

Convergence Theorems

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Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence

Georgian Mathematical Journal ◽

10.1515/gmj.2002.431 ◽

2002 ◽

Vol 9 (3) ◽

pp. 431-448

Author(s):

A. Bychowska

Keyword(s):

Cauchy Problem ◽

Parabolic Equations ◽

Unknown Function ◽

Functional Dependence ◽

Nonlinear Parabolic Equations ◽

Quasilinearization Method ◽

Convergence Theorems ◽

Nonlinear Parabolic ◽

Quasilinearization Methods ◽

Derivatives Of

Abstract We consider a Cauchy problem for nonlinear parabolic equations with functional dependence. We prove convergence theorems for a general quasilinearization method in two cases: (i) the Hale functional acting only on the unknown function, (ii) including partial derivatives of the unknown function.

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