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Open AccessArticle

Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations

1
National Institute of Technology, Jalandhar 144011, India
2
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain
3
Department of Mathematics, L. N. M. U. Darbhanga-Bihar, Darbhanga 846004, India
4
Department of Mathematics, I.I.T Kharagpur, Kharagpur 721302, India
*
Author to whom correspondence should be addressed.
This Paper is an Extended Version of Our Paper Published in Mathematical Modelling in Engineering and Human Behavior 2017.
Mathematics 2020, 8(3), 384; https://doi.org/10.3390/math8030384 (registering DOI)
Received: 14 February 2020 / Revised: 2 March 2020 / Accepted: 3 March 2020 / Published: 9 March 2020
In this work, we performed an study about the domain of existence and uniqueness for an efficient fifth order iterative method for solving nonlinear problems treated in their infinite dimensional form. The hypotheses for the operator and starting guess are weaker than in the previous studies. We assume omega continuity condition on second order Fréchet derivative. This fact it is motivated by showing different problems where the nonlinear operators that define the equation do not verify Lipschitz and Hölder condition; however, these operators verify the omega condition established. Then, the semilocal convergence balls are obtained and the R-order of convergence and error bounds can be obtained by following thee main theorem. Finally, we perform a numerical experience by solving a nonlinear Hammerstein integral equations in order to show the applicability of the theoretical results by obtaining the existence and uniqueness balls. View Full-Text
Keywords: semilocal convergence; Lipschitz condition; Hölder condition; Hammerstein integral equation; dynamical systems semilocal convergence; Lipschitz condition; Hölder condition; Hammerstein integral equation; dynamical systems
MDPI and ACS Style

Singh, S.; Martínez, E.; Kumar, A.; Gupta, D.K. Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations. Mathematics 2020, 8, 384.

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