Solving Hammerstein-Type Integral Equations with Polynomial Nemystkii Operator

被引：0

作者：

Hernandez-Veron, M. A. ^{[1
]}

Yadav, Sonia ^{[2
]}

Martinez, Eulalia ^{[3
]}

Singh, Sukhjit ^{[2
]}

机构：

[1] Univ La Rioja, Dept Math & Computat, Logrono, Spain

[2] Dr BR Ambedkar Natl Inst Technol, Jalandhar, India

[3] Univ Politecn Valencia, Inst Univ Matemat Multidisciplinar, Valencia, Spain

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2025年 / 22卷 / 03期

关键词：

Hammerstein-type non-linear integral equations; family of third-order iterative methods; convergence; recurrence relations; FREDHOLM;

D O I：

10.1007/s00009-025-02830-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this study, we use a family of third-order iterative methods to locate, separate, and approximate a solution of non-linear integral equations of Hammerstein type. We will consider two situations, when the kernel of the integral equation is separable and when it is not separable. When the kernel is non-separable, we will approximate the given integral equation by means of a new one with a separable kernel, and this transformation allows us to locate and approximate a solution of the first integral equation. To apply our theoretical findings, various examples have been tested.

引用

页数：18

共 50 条

[21] Application of an inverse-free Jarratt-type approximation to nonlinear integral equations of Hammerstein-type
Univ of La Rioja, Logrono, Spain
Comput Math Appl, 4 (9-20):
[22] The application of an inverse-free Jarratt-type approximation to nonlinear integral equations of Hammerstein-type
Ezquerro, JA
Gutierrez, JM
Hernandez, MA
Salanova, MA
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 36 (04) : 9 - 20
[23] FIXED POINTS OF HAMMERSTEIN-TYPE EQUATIONS ON GENERAL CONES
Figueroa, Ruben
Tojo, F. Adrian F.
FIXED POINT THEORY, 2018, 19 (02): : 571 - 586
[24] Iterative regularization methods for ill-posed Hammerstein-type operator equations in Hilbert scales
Argyros, Ioannis K.
George, Santhosh
Kunhanandan, M.
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2014, 59 (02): : 247 - 262
[25] Uniqueness and existence of positive solutions for Hammerstein integral equations of polynomial type
Zhao, ZQ
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 32 (06) : 795 - 805
[26] On nonlinear Fredholm integral equations with non-differentiable Nemystkii operator
Hernandez-Veron, M. A.
Martinez, Eulalia
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (14) : 7961 - 7976
[27] On the solvability of a system of nonlinear integral equations with a monotone Hammerstein type operator
Khachatryan, Kh. A.
Petrosyan, H. S.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2022, 28 (02): : 201 - 214
[28] Strong and weak convergence theorems for solutions of equations of Hammerstein-type
Ofoedu, Eric U.
Osigwe, Chimezie B.
Ibeh, Kingsley O.
Madu, Lovelyn O.
FILOMAT, 2023, 37 (02) : 477 - 490
[29] A modified Newton-Lavrentiev regularization for nonlinear ill-posed Hammerstein-type operator equations
George, Santhosh
Nair, A. Thamban
JOURNAL OF COMPLEXITY, 2008, 24 (02) : 228 - 240
[30] An extension of invertibility of Hammerstein-type operators
Tunaru, R
CZECHOSLOVAK MATHEMATICAL JOURNAL, 1999, 49 (02) : 341 - 346

← 1 2 3 4 5 →