Local convergence of two Newton-like methods under Holder continuity condition in Banach spaces

2020 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
S.K. Parhi ◽  
Debasis Sharma
Keyword(s):  
Banach Spaces ◽  
Local Convergence ◽  
Hölder Continuity ◽  
Continuity Condition ◽  
Holder Continuity

ON THE R-ORDER CONVERGENCE OF A THIRD ORDER METHOD IN BANACH SPACES UNDER MILD DIFFERENTIABILITY CONDITIONS

2009 ◽  
Vol 06 (02) ◽  
pp. 291-306 ◽  
Author(s):  
P. K. PARIDA ◽  
D. K. GUPTA
Keyword(s):  
Banach Spaces ◽  
Recurrence Relations ◽  
Hölder Continuity ◽  
A Priori ◽  
Continuity Condition ◽  
Order Method ◽  
Holder Continuity ◽  
Third Order ◽  
A Priori Error Bounds ◽  
Two Parameters

The aim of this paper is to discuss the convergence of a third order method for solving nonlinear equations F(x)=0 in Banach spaces by using recurrence relations. The convergence of the method is established under the assumption that the second Fréchet derivative of F satisfies a condition that is milder than Lipschitz/Hölder continuity condition. A family of recurrence relations based on two parameters depending on F is also derived. An existence-uniqueness theorem is also given that establish convergence of the method and a priori error bounds. A numerical example is worked out to show that the method is successful even in cases where Lipschitz/Hölder continuity condition fails.

A centred norm inequality for singular integral operators

1992 ◽  
Vol 112 (2) ◽  
pp. 369-383
Author(s):  
Richard F. Bass
Keyword(s):  
Singular Integral ◽  
Hölder Continuity ◽  
Integral Kernel ◽  
Integral Operators ◽  
Continuity Condition ◽  
Norm Inequality ◽  
Singular Integral Operators ◽  
Holder Continuity ◽  
The Mean

AbstractLet K be a standard singular integral kernel on ℝ satisfying the usual Hölder continuity condition of order δ, and define (where c is chosen so that the integral of w is 1), the mean of g with respect to the measure w(x) dx, and ‖·‖p the Lp norm with respect to w(x) dx. Although the inequality is not true in general, the centred norm inequality does hold for 1 < p < ∞ if α < δ.

scholarly journals Intrinsic Square Function Characterizations of Variable Hardy–Lorentz Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Khedoudj Saibi
Keyword(s):  
Measurable Function ◽  
Lorentz Space ◽  
Hölder Continuity ◽  
Continuity Condition ◽  
Lorentz Spaces ◽  
Square Function ◽  
Holder Continuity ◽  
Area Function ◽  
Intrinsic Square Function ◽  
Lusin Area Function

The aim of this paper is to establish the intrinsic square function characterizations in terms of the intrinsic Littlewood–Paley g-function, the intrinsic Lusin area function, and the intrinsic gλ∗-function of the variable Hardy–Lorentz space Hp⋅,qℝn, for p⋅ being a measurable function on ℝn satisfying 0<p−≔ess infx∈ℝnpx≤ess supx∈ℝnpx≕p+<∞ and the globally log-Hölder continuity condition and q∈0,∞, via its atomic and Littlewood–Paley function characterizations.

Some properties of Musielak spaces with only the log-Hölder continuity condition and application

2020 ◽  
Vol 11 (4) ◽  
pp. 1062-1080
Author(s):  
Mustafa Ait Khellou ◽  
Abdelmoujib Benkirane ◽  
Sidi Mohamed Douiri
Keyword(s):  
Hölder Continuity ◽  
Continuity Condition ◽  
Holder Continuity

On the local convergence of Weerakoon–Fernando method with $$\omega $$ continuity condition in Banach spaces

SeMA Journal ◽  
2020 ◽  
Vol 77 (3) ◽  
pp. 291-304 ◽  
Author(s):  
Ioannis K. Argyros ◽  
Debasis Sharma ◽  
Sanjaya Kumar Parhi
Keyword(s):  
Banach Spaces ◽  
Local Convergence ◽  
Continuity Condition
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