scholarly journals A new shrinking iterative scheme for d-accretive mappings with applications to capillarity systems

2020 ◽  
Vol 2020 (1) ◽  
Keyword(s):  
Iterative Scheme ◽  
Accretive Mappings

scholarly journals Path Convergence and Approximation of Common Zeroes of a Finite Family ofm-Accretive Mappings in Banach Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Yekini Shehu ◽  
Jerry N. Ezeora
Keyword(s):  
Real Banach Space ◽  
Iterative Scheme ◽  
Finite Family ◽  
Duality Mapping ◽  
Strong Convergence Theorem ◽  
Sunny Nonexpansive Retraction ◽  
Mild Conditions ◽  
Pseudocontractive Mappings ◽  
Uniformly Smooth ◽  
Accretive Mappings

LetEbe a real Banach space which is uniformly smooth and uniformly convex. LetKbe a nonempty, closed, and convex sunny nonexpansive retract ofE, whereQis the sunny nonexpansive retraction. IfEadmits weakly sequentially continuous duality mappingj, path convergence is proved for a nonexpansive mappingT:K→K. As an application, we prove strong convergence theorem for common zeroes of a finite family ofm-accretive mappings ofKtoE. As a consequence, an iterative scheme is constructed to converge to a common fixed point (assuming existence) of a finite family of pseudocontractive mappings fromKtoEunder certain mild conditions.

Secant-type iteration for nonlinear ill-posed equations in Banach space

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Santhosh George ◽  
C. D. Sreedeep ◽  
Ioannis K. Argyros
Keyword(s):  
Iterative Scheme ◽  
Regularization Parameter ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Adaptive Parameter ◽  
Choice Strategy ◽  
Accretive Mappings ◽  
Ill Posed ◽  
Adaptive Parameter Choice Strategy ◽  
Parameter Choice Strategy

Abstract In this paper, we study secant-type iteration for nonlinear ill-posed equations involving 𝑚-accretive mappings in Banach spaces. We prove that the proposed iterative scheme has a convergence order at least 2.20557 using assumptions only on the first Fréchet derivative of the operator. Further, using a general Hölder-type source condition, we obtain an optimal error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter.

scholarly journals Iterative Scheme with Errors for Common Zeros of Finite Accretive Mappings and Nonlinear Elliptic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Li Wei ◽  
Ruilin Tan
Keyword(s):  
Banach Space ◽  
Real Banach Space ◽  
Iterative Scheme ◽  
Elliptic Systems ◽  
Iterative Sequence ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic ◽  
Accretive Mappings ◽  
The Relationship ◽  
Common Zeros

We present a new iterative scheme with errors to solve the problems of finding common zeros of finitem-accretive mappings in a real Banach space. Strong convergence theorems are established, which extend the corresponding works given by some authors. Moreover, the relationship between zeros ofm-accretive mappings and one kind of nonlinear elliptic systems is investigated, from which we can see that some restrictions imposed on the iterative scheme are valid and the solution of one kind of nonlinear elliptic systems can be approximated by a suitably defined iterative sequence.

scholarly journals Inertial Iterative Schemes for D-Accretive Mappings in Banach Spaces and Curvature Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Li Wei ◽  
Wenwen Yue ◽  
Yingzi Shang ◽  
Ravi P. Agarwal
Keyword(s):  
Banach Space ◽  
Iterative Scheme ◽  
Zero Point ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
New Techniques ◽  
Numerical Examples ◽  
Iterative Schemes ◽  
Uniformly Smooth ◽  
Accretive Mappings

We propose and analyze a new iterative scheme with inertial items to approximate a common zero point of two countable d-accretive mappings in the framework of a real uniformly smooth and uniformly convex Banach space. We prove some strong convergence theorems by employing some new techniques compared to the previous corresponding studies. We give some numerical examples to illustrate the effectiveness of the main iterative scheme and present an example of curvature systems to emphasize the importance of the study of d-accretive mappings.

A two-scale iterative scheme for a phase-field model for precipitation and dissolution in porous media

2021 ◽  
Vol 396 ◽  
pp. 125933
Author(s):  
Manuela Bastidas Olivares ◽  
Carina Bringedal ◽  
Iuliu Sorin Pop
Keyword(s):  
Porous Media ◽  
Phase Field ◽  
Field Model ◽  
Iterative Scheme ◽  
Phase Field Model
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