Extended Newton-type Method for Nonsmooth Generalized Equation under <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mfenced open="(" close=")" separators="|"> <mrow> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </mfenced> </math>-point-based Approximation
نویسندگان
چکیده
Let X and id="M3"> mathvariant="script">Y be Banach spaces id="M4"> mathvariant="script">Ω ⊆ X . id="M5"> f : ⟶ a single valued function which is nonsmooth. Suppose that id="M6"> F mathvariant="script">X⇉ 2 set-valued mapping has closed graph. In the present paper, we study extended Newton-type method for solving nonsmooth generalized equation id="M7"> 0 ∈ x + analyze its semilocal local convergence under conditions id="M8"> − 1 Lipschitz-like id="M9"> admits certain type of approximation generalizes concept point-based so-called id="M10"> n , α -point-based approximation. Applications id="M11"> are provided smooth functions in cases id="M12"> = id="M13"> as well normal maps. particular, when id="M14"> < derivative id="M15"> , denoted id="M16"> ∇ id="M17"> ℓ -Hölder continuous, have shown id="M18"> id="M19"> id="M20"> while id="M21"> id="M22"> id="M23"> id="M24"> second id="M25"> id="M26"> id="M27"> K -Hölder. Moreover, constructed an id="M28"> maps id="M29"> mathvariant="script">C id="M30"> id="M31"> Finally, numerical experiment to validate theoretical result this study.
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2022
ISSN: ['1687-0425', '0161-1712']
DOI: https://doi.org/10.1155/2022/7108996