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Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 2/2023

08.10.2022 | Original Research

New iterative methods for finding solutions of Hammerstein equations

verfasst von: Oganeditse A. Boikanyo, Habtu Zegeye

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 2/2023

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Abstract

Let \(G:H\rightarrow H\) and \(K: H\rightarrow H\) be monotone mappings that are either sequentially weakly continuous or continuous, where H is a real Hilbert space. In this work, we introduce two new iterative methods for approximating solutions of the Hammerstein equation \(u+GKu=0\), if they exist. The first iterative method is shown to always converge weakly to an element in the solution set of the Hammerstein equation if this solution set is nonempty. The second iterative method is a modification of the first method to upgrade weak convergence to strong convergence. Convergence results are obtained without requiring the maps to be bounded. Numerical examples are provided to demonstrate the convergence of one of these methods. Comparisons with some existing methods show that the method is cost effective in terms of the number of iterations required to obtain a solution and the computational time.
Vorheriger Artikel A denoising model based on the fractional Beltrami regularization and its numerical solution
Nächster Artikel A modified stochastic quasi-Newton algorithm for summing functions problem in machine learning

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Literatur
1.
2.
Appell, J., Benavides, T.D.: Nonlinear Hammerstein equations and functions of bounded Riesz–Medvedev variation. Topol. Methods Nonlinear Anal. 47, 319–332 (2016)MathSciNetMATH
3.
Bello, A.U., Omojola, M.T., Yahaya, J.: An inertial-type algorithm for approximation of solutions of Hammerstein integral inclusions in Hilbert spaces. Fixed Point Theory Algorithms Sci. Eng. 2021(8), 22 (2021)MathSciNetMATH
4.
Blum, E., Oettli, W.: From optimization and variational inequality to equilibrium problems. Math. Stud. 63, 123–145 (1994)MATH
5.
Boikanyo, O.A.: The generalized contraction proximal point algorithm with square-summable errors. Afr. Mat. 28, 321–332 (2017) MathSciNetMATH
6.
Brézis, H., Browder, F.E.: Some new results about Hammerstein equations. Bull. Am. Math. Soc. 80, 568–572 (1974)MathSciNetMATH
7.
Brézis, H., Browder, F.E.: Existence theorems for nonlinear integral equations of Hammerstein type. Bull. Am. Math. Soc. 81, 73–78 (1975)MathSciNetMATH
8.
Brézis, H., Browder, F.E.: Nonlinear integral equations and systems of Hammerstein type. Adv. Math. 18, 115–147 (1975)MathSciNetMATH
9.
Browder, F.E.: The solvability of nonlinear functional equations. Duke Math. J. 30, 557–566 (1963)MathSciNetMATH
10.
Browder, F.E.: Nonlinear mappings of non-expansive and accretive operators in Banach spaces. Bull. Am. Math. Soc. 73, 875–882 (1967)MATH
11.
Browder, F.E.: Nonlinear functional analysis and nonlinear integral equations of Hammerstein and Urysohn type. In: Zarantonello, E. (ed.) Contributions to Nonlinear Functional Analysis, pp. 425–500. Academic Press, New York (1971)
12.
Browder, F.E., Gupta, C.P.: Nonlinear monotone operators and integral equations of Hammerstein type. Bull. Am. Math. Soc. 75, 1347–1353 (1969)MATH
13.
Browder, F.E., De Figueiredo, D.G., Gupta, C.P.: Maximal monotone operators and nonlinear integral equations of Hammerstein type. Bull. Am. Math. Soc. 76, 700–705 (1970)MathSciNetMATH
14.
Chepanovich, R.S.: Nonlinear Hammerstein equations and fixed points. Publ. Inst. Math. (Belgr.) 35, 119–123 (1984)MathSciNet
15.
Chidume, C.E., Bello, A.U.: An iterative algorithm for approximating solutions of Hammerstein equations with monotone maps in Banach spaces. Appl. Math. Comput. 313, 408–417 (2017)MathSciNetMATH
16.
Chidume, C.E., Djitte, N.: Iterative approximation of solutions of nonlinear equations of Hammerstein-type. Nonlinear Anal. 70, 4086–4092 (2009)MathSciNetMATH
17.
Chidume, C.E., Djitte, N.: Approximation of solutions of Hammerstein equations with bounded strongly accretive nonlinear operator. Nonlinear Anal. 70, 4071–4078 (2009)MathSciNetMATH
18.
Chidume, C.E., Djitte, N.: An iterative method for solving nonlinear integral equations of Hammerstein type. Appl. Math. Comput. 219, 5613–5621 (2013)MathSciNetMATH
19.
20.
Chidume, C.E., Ofoedu, E.U.: Solution of nonlinear integral equations of Hammerstein type. Nonlinear Anal. 74, 4293–4299 (2011)MathSciNetMATH
21.
Chidume, C.. E., Shehu, Y.: Strong convergence theorem for approximation of solutions of equations of Hammerstein type. Nonlinear Anal. Theory Methods Appl. 75(14), 5664–5671 (2012)MathSciNetMATH
22.
Chidume, C.E., Shehu, Y.: Approximation of solutions of generalized equations of Hammerstein type. Comput. Math. Appl. 63, 966–974 (2012)MathSciNetMATH
23.
Chidume, C.E., Shehu, Y.: Iterative approximation of solutions of equations of Hammerstein type in certain Banach spaces. Appl. Math. Comput. 219, 5657–5667 (2013)MathSciNetMATH
24.
Chidume, C.E., Shehu, Y.: Approximation of solutions of equations Hammerstein type in Hilbert spaces. Fixed Point Theory 16(1), 91–102 (2015)MathSciNetMATH
25.
Chidume, C.E., Zegeye, H.: Approximation of solutions of nonlinear equations of monotone and Hammerstein-type. Appl. Anal. 82(8), 747–758 (2003)MathSciNetMATH
26.
Chidume, C.E., Zegeye, H.: Iterative approximation of solutions of nonlinear equation of Hammerstein-type. Abstr. Appl. Anal. 6, 353–367 (2003)MathSciNetMATH
27.
Chidume, C.E., Zegeye, H.: Approximation of solutions nonlinear equations of Hammerstein type in Hilbert space. Proc. Am. Math. Soc. 133, 851–858 (2005)MathSciNetMATH
28.
Chidume, C.E., Adamu, A., Chinwendu, L.O.: Approximation of solutions of Hammerstein equations with monotone mappings in real Banach spaces. Carpath. J. Math. 35(3), 305–316 (2019)MathSciNetMATH
29.
30.
31.
Daman, O., Tufa, A.R., Zegeye, H.: Approximating solutions of Hammerstein type equations in Banach spaces. Quaest. Math. 42(5), 561–577 (2019)MathSciNetMATH
32.
De Figueiredo, D.G., Gupta, C.P.: On the variational methods for the existence of solutions to nonlinear equations of Hammerstein type. Bull. Am. Math. Soc. 40, 470–476 (1973)MathSciNet
33.
Djitte, N., Sene, M.: An iterative algorithm for approximating solutions of Hammerstein integral equations. Numer. Funct. Anal. Optim. 34(12), 1299–1316 (2013)MathSciNetMATH
34.
Dolezal, V.: Monotone operators and applications in control and network theory. In: Studies in Automation and Control, Vol. 2. Elsevier Scientific, New York (1978)
35.
Goebel, K., Kirk, W.A.: Topics on Metric Fixed Point Theory. Cambridge University Press, Cambridge (1990)MATH
36.
Kazemi, M.: Triangular functions for numerical solution of the nonlinear Volterra integral equations. J. Appl. Math. Comput. 1–24 (2021)
37.
Kazemi, M.: On existence of solutions for some functional integral equations in Banach algebra by fixed point theorem. Int. J. Nonlinear Anal. Appl. 13(1), 451–466 (2022)
38.
Kazemi, M., Ezzati, R.: Existence of solution for some nonlinear two-dimensional Volterra integral equations via measures of noncompactness. Appl. Math. Comput. 275, 165–171 (2016)MathSciNetMATH
39.
40.
Maingé, P.E.: Strong convergence of projected subgradiant method for nonsmooth and nonstrictily convex minimization. Set-Valued Anal. 16, 899–912 (2008)MathSciNetMATH
41.
Micula, S., Cattani, C.: On a numerical method based on wavelets for Fredholm–Hammerstein integral equations of the second kind. Math. Methods Appl. Sci. 41, 9103–9115 (2018)MathSciNetMATH
42.
Minjibir, M.S., Mohammed, I.: Iterative algorithms for solutions of Hammerstein integral inclusions. Appl. Math. Comput. 320, 389–399 (2018)MathSciNetMATH
43.
Neamprem, K., Klangrak, A., Kaneko, H.: Taylor–Series expansion methods for multivariate Hammerstein integral equations. Int. J. Appl. Math. 47(4), 1–5 (2017)MathSciNet
44.
Ofoedu, E.U., Onyi, C.E.: New implicit and explicit approximation methods for solutions of integral equations of Hammerstein type. Appl. Math. Comput. 246, 628–637 (2014)MathSciNetMATH
45.
Opial, Z.: Weak convergence of the sequence of successive approximations for non-expansive mappings. Bull. Am. Math. Soc. 73, 591–597 (1967)MATH
46.
Pascali, D., Sburlan, S.: Nonlinear mappings of monotone type. Editura Academia, Bucharest (1978)MATH
47.
Shehu, Y.: Strong convergence theorem for integral equations of Hammerstein type in Hilbert spaces. Appl. Math. Comput. 231, 140–147 (2014)MathSciNetMATH
48.
Tufa, A.R., Zegeye, H., Thuto, M.: Iterative solutions of nonlinear integral equations of Hammerstein type. Int. J. Anal. Appl. 9(2), 129–141 (2015)MATH
49.
Uba, M.O., Uzochukwu, M.I., Onyido, M.A.: Algorithm for approximating solutions of Hammerstein integral equations with maximal monotone operators. Indian J. Pure Appl. Math. 48(3), 391–410 (2017)MathSciNetMATH
50.
51.
Xu, H.K.: Another control condition in an iterative method for nonexpansive mappings. Bull. Aust. Math. Soc. 65, 109–113 (2002)MathSciNetMATH
52.
Zegeye, H., Malonza, D.M.: Hybrid approximation of solutions of integral equations of the Hammerstein type. Arab. J. Math. 2, 221–232 (2013)MathSciNetMATH
Metadaten
Titel
New iterative methods for finding solutions of Hammerstein equations
verfasst von
Oganeditse A. Boikanyo
Habtu Zegeye
Publikationsdatum
08.10.2022
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 2/2023
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-022-01795-y

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