scholarly journals Strong convergence and stability of Picard iteration sequences for a general class of contractive-type mappings

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Charles E Chidume
Keyword(s):  
Strong Convergence ◽  
General Class ◽  
Picard Iteration ◽  
Convergence And Stability ◽  
Contractive Type

scholarly journals Some results of the Picard-Krasnoselskii hybrid iterative process

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 359-365
Author(s):  
Aynur Şahin
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Strong Convergence ◽  
Hyperbolic Space ◽  
General Class ◽  
Iterative Process ◽  
Convergence And Stability ◽  
Stability Results

In this paper, we establish the strong convergence and stability results of Picard-Krasnoselskii hybrid iterative process for a general class of contractive-like operators in a hyperbolic space. Additionally, we apply this iterative process to obtain the solution of a functional equation in a Banach space.

scholarly journals Convergence and Stability of New Approximation Algorithms for Certain Contractive-Type Mappings

2021 ◽  
Vol 2 ◽  
pp. 1
Author(s):  
Imo Kalu Agwu ◽  
Donatus Ikechi Igbokwe
Keyword(s):  
Approximation Algorithms ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Type Condition ◽  
Iterative Schemes ◽  
Convergence And Stability ◽  
Contractive Type ◽  
Stability Results

We present new fixed points algorithms called multistep H-iterative scheme and multistep SH-iterative scheme. Under certain contractive-type condition, convergence and stability results were established without any imposition of the ’sum conditions’, which to a large extent make some existing iterative schemes so far studied by other authors in this direction practically inefficient. Our results complement and improve some recent results in literature.

scholarly journals STRONG CONVERGENCE THEOREMS FOR A QUASI CONTRACTIVE TYPE MAPPING EMPLOYING A NEW ITERATIVE SCHEME WITH AN APPLICATION

2017 ◽  
Vol 39 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Surjeet Singh Chauhan ◽  
Kiran Utreja ◽  
Mohammad Imdad ◽  
Md Ahmadullah
Keyword(s):  
Strong Convergence ◽  
Iterative Scheme ◽  
Convergence Theorems ◽  
Type Mapping ◽  
Contractive Type

Practicably Optimal Point and its Solution in Deterministic System

2012 ◽  
Vol 190-191 ◽  
pp. 143-146
Author(s):  
Ruo Ping Li ◽  
Xiang Yong Kong ◽  
Li Qun Gao ◽  
De Xuan Zou
Keyword(s):  
Particle Swarm Optimization ◽  
Strong Convergence ◽  
Objective Function ◽  
Particle Swarm ◽  
Deterministic System ◽  
Optimal Point ◽  
Swarm Optimization ◽  
Convergence And Stability ◽  
Efficient Alternative ◽  
Global Optimal

In some cases, it’s not enough to consider only the objective function of the global optimal point, but also the character of this point and its nearby area. To this end, the concept of practicably optimal point is introduced in this paper. Further, a novel intelligence method named simulated particle swarm optimization (NSPSO) algorithm is proposed to obtain the practicably optimal points according to different requirements. The optimization results reveal that the NSPSO algorithm has strong convergence and stability, and appears to be an efficient alternative for obtaining the practicably optimal points according to different requirements.

scholarly journals Descent methods for convex optimization problems in Banach spaces

2005 ◽  
Vol 2005 (15) ◽  
pp. 2347-2357
Author(s):  
M. S. S. Ali
Keyword(s):  
Convex Optimization ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Methods ◽  
General Class ◽  
Optimization Problems ◽  
Initial Problem ◽  
Descent Methods ◽  
Convex Optimization Problems ◽  
Convexity Properties

We consider optimization problems in Banach spaces, whose cost functions are convex and smooth, but do not possess strengthened convexity properties. We propose a general class of iterative methods, which are based on combining descent and regularization approaches and provide strong convergence of iteration sequences to a solution of the initial problem.

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