A Stirling-like method with Hölder continuous first derivative in Banach spaces |
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Authors: | SK Parhi DK Gupta |
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Institution: | Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India |
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Abstract: | In this paper, the convergence of a Stirling-like method used for finding a solution for a nonlinear operator in a Banach space is examined under the relaxed assumption that the first Fréchet derivative of the involved operator satisfies the Hölder continuity condition. Many results exist already in the literature to cover the stronger case when the second Fréchet derivative of the involved operator satisfies the Lipschitz/Hölder continuity condition. Our convergence analysis is done by using recurrence relations. The error bounds and the existence and uniqueness regions for the solution are obtained. Finally, two numerical examples are worked out to show that our convergence analysis leads to better error bounds and existence and uniqueness regions for the fixed points. |
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Keywords: | Stirling-like method Hö lder continuity condition Fré chet derivative Nonlinear operator equations |
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