On the convergence of a certain class of iterative procedures under relaxed conditions with applications |
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Institution: | Department of Mathematics, Cameron University, 2800 West Gore, Lawton, OK 73505, United States |
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Abstract: | We provide sufficient convergence conditions for a certain class of inexact Newton-like methods to a locally unique solution of a nonlinear equation in a Banach space. The equation contains a nondifferentiable term and at each step we use the inverse of the same linear operator. We use Ptak-like conditions that are weaker than earlier ones. Our results apply whenever earlier ones do but not vice versa. A semilocal convergence result is also given based on the contraction mapping principle. Finally, our results apply to solve a nonlinear integral equation of Uryson type appearing in elasticity theory that cannot be solved with existing methods. |
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