Some convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operators [PDF]
Mathematica Bohemica, 2019 We study some qualitative features like convergence, stability and data dependency for Picard-S iteration method of a quasi-strictly contractive operator under weaker conditions imposed on parametric sequences in the mentioned method. We compare the rate
Müzeyyen Ertürk, Faik Gürsoy
doaj +4 more sources
On T-Stability of Picard Iteration in Cone Metric Spaces [PDF]
Fixed Point Theory and Applications, 2009 The aim of this work is to investigate the T-stability of Picard's iteration procedures in cone metric spaces and give an application.
B. E. Rhoades +3 more
doaj +2 more sources
On T-Stability of the Picard Iteration for Generalized φ-Contraction Mappings [PDF]
Abstract and Applied Analysis, 2012 We introduce some results on T-stability of the Picard iteration for φ-contraction and generalized φ-contraction mappings on metric spaces.
R. H. Haghi, M. Postolache, Sh. Rezapour
doaj +2 more sources
Modelling iteration in engineering design [PDF]
, 2012 This paper examines design iteration and its modelling in the simulation of New Product Development (NPD) processes. A framework comprising six perspectives of iteration is proposed and it is argued that the importance of each perspective depends upon ...
Eckert, C. M. +2 more
core +9 more sources
A PICARD THEOREM FOR ITERATIVE DIFFERENTIAL EQUATIONS [PDF]
Demonstratio Mathematica, 2009 AbstractA Picard type existence and uniqueness theorem is established for iterative differential equations of the ...
Li, Wenrong, Cheng, Sui Sun
openaire +2 more sources
Weak Convergence of Two Iteration Schemes in Banach Spaces [PDF]
Engineering and Technology Journal, 2019 In this paper, we established weak convergence theorems by using appropriate conditions for approximating common fixed points and equivalence between the convergence of the Picard-Mann iteration scheme and Liu et al iteration scheme in Banach spaces.
Salwa Abed, Zahraa Mohamed Hasan
doaj +1 more source
Approximation of Fixed Points for Mean Nonexpansive Mappings in Banach Spaces
Journal of Function Spaces, 2021 In this paper, we establish weak and strong convergence theorems for mean nonexpansive maps in Banach spaces under the Picard–Mann hybrid iteration process.
Junaid Ahmad +3 more
doaj +1 more source
A modification of the convergence conditions for Picard's iteration [PDF]
Computational & Applied Mathematics, 2004 To solve by successive approximation nonlinear equations of the form F(x)=0, where F:Ω⊆X→X, is an operator defined on an open convex domain of a Banach space X with values in X, one uses a fixed point theorem based method which requires the operator G(x)=x−F(x) to be a contraction. This has a very limited scope of applicability.
Ezquerro, J. A., Hernández, M. A.
openaire +5 more sources
Mandelbrot Sets and Julia Sets in Picard-Mann Orbit
IEEE Access, 2020 The purpose of this paper is to introduce the Mandelbrot and Julia sets by using Picard-Mann iteration procedure. Escape criteria is established which plays an important role to generate Mandelbrot and Julia sets.
Cui Zou +4 more
doaj +1 more source
Iterative approximation of fixed points of contraction mappings in complex valued Banach spaces
Arab Journal of Mathematical Sciences, 2019 We approximate the fixed points of contraction mappings using the Picard–Krasnoselskii hybrid iterative process, which is known to converge faster than all of Picard, Mann and Ishikawa iterations in complex valued Banach spaces.
Godwin Amechi Okeke
doaj +1 more source