Convergence of some kind of Jungck iterative scheme for two self-mappings in n-Banach space

2021 ◽  
pp. 1-6
Author(s):  
Enas Dawood Salman ◽  
Zeana Zaki Jamil
Keyword(s):  
Banach Space ◽  
Iterative Scheme

scholarly journals Estimation of Newly Established Iterative Scheme for Generalized Nonexpansive Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Aftab Hussain ◽  
Nawab Hussain ◽  
Danish Ali
Keyword(s):  
Banach Space ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Space Environment ◽  
Iterative Approach ◽  
Uniformly Convex ◽  
Prior Art ◽  
Nonexpansive Maps ◽  
New Iterative Method

We introduce a new iterative method in this article, called the D iterative approach for fixed point approximation. Analytically, and also numerically, we demonstrate that our established D I.P is faster than the well-known I.P of the prior art. Finally, in a uniformly convex Banach space environment, we present weak as well as strong convergence theorems for Suzuki’s generalized nonexpansive maps. Our findings are an extension, refinement, and induction of several existing iterative literatures.

scholarly journals On Common Random Fixed Points of a New Iteration with Errors for Nonself Asymptotically Quasi-Nonexpansive Type Random Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
R. A. Rashwan ◽  
P. K. Jhade ◽  
Dhekra Mohammed Al-Baqeri
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Separable Banach Space ◽  
Iterative Scheme ◽  
Random Fixed Points ◽  
Real Separable Banach Space ◽  
Random Mappings

We prove some strong convergence of a new random iterative scheme with errors to common random fixed points for three and then N nonself asymptotically quasi-nonexpansive-type random mappings in a real separable Banach space. Our results extend and improve the recent results in Kiziltunc, 2011, Thianwan, 2008, Deng et al., 2012, and Zhou and Wang, 2007 as well as many others.

scholarly journals A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 271 ◽  
Author(s):  
Ramandeep Behl ◽  
Ioannis K. Argyros
Keyword(s):  
Mathematical Modeling ◽  
Banach Space ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Iterative Scheme ◽  
Real Life ◽  
System Of Nonlinear Equations ◽  
Life Problems ◽  
Lipschitz Constants ◽  
Better Than

Many real-life problems can be reduced to scalar and vectorial nonlinear equations by using mathematical modeling. In this paper, we introduce a new iterative family of the sixth-order for a system of nonlinear equations. In addition, we present analyses of their convergences, as well as the computable radii for the guaranteed convergence of them for Banach space valued operators and error bounds based on the Lipschitz constants. Moreover, we show the applicability of them to some real-life problems, such as kinematic syntheses, Bratu’s, Fisher’s, boundary value, and Hammerstein integral problems. We finally wind up on the ground of achieved numerical experiments, where they perform better than other competing schemes.

scholarly journals On Best Proximity Results for a Generalized Modified Ishikawa’s Iterative Scheme Driven by Perturbed 2-Cyclic Like-Contractive Self-Maps in Uniformly Convex Banach Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
M. De la Sen ◽  
Mujahid Abbas
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Convex Banach Space ◽  
The Self ◽  
Uniformly Convex ◽  
Cyclic Structure ◽  
Best Proximity Points ◽  
Uniformly Convex Banach Spaces

This paper proposes a generalized modified iterative scheme where the composed self-mapping driving can have distinct step-dependent composition order in both the auxiliary iterative equation and the main one integrated in Ishikawa’s scheme. The self-mapping which drives the iterative scheme is a perturbed 2-cyclic one on the union of two sequences of nonempty closed subsets Ann=0∞ and Bnn=0∞ of a uniformly convex Banach space. As a consequence of the perturbation, such a driving self-mapping can lose its cyclic contractive nature along the transients of the iterative process. These sequences can be, in general, distinct of the initial subsets due to either computational or unmodeled perturbations associated with the self-mapping calculations through the iterative process. It is assumed that the set-theoretic limits below of the sequences of sets Ann=0∞ and Bnn=0∞ exist. The existence of fixed best proximity points in the set-theoretic limits of the sequences to which the iterated sequences converge is investigated in the case that the cyclic disposal exists under the asymptotic removal of the perturbations or under its convergence of the driving self-mapping to a limit contractive cyclic structure.

scholarly journals A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-31 ◽  
Author(s):  
Siwaporn Saewan ◽  
Poom Kumam
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Generalized Mixed Equilibrium Problem ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality for anα-inverse-strongly monotone operator, the set of solutions of the generalized mixed equilibrium problem and zeros of a maximal monotone operator in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2 uniformly convex and uniformly smooth Banach space. The results presented in this paper improve and extend some recent results.

scholarly journals Convergence of Common Random Fixed Point of Finite Family of Asymptotically Quasi-Nonexpansive-Type Mappings by an Implicit Random Iterative Scheme

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
A. S. Saluja ◽  
Pankaj kumar Jhade
Keyword(s):  
Banach Space ◽  
Iterative Scheme ◽  
Sufficient Conditions ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Finite Family ◽  
Uniformly Convex ◽  
Random Fixed Point ◽  
Random Iteration ◽  
Necessary And Sufficient

We introduce a new implicit random iteration process generated by a finite family of asymptotically quasi-nonexpansive-type mappings and study necessary and sufficient conditions for the convergence of this process in a uniformly convex Banach space. The results presented in this paper extend and improve the recent ones announced by Plubtieng et al. (2007), Beg and Thakur (2009), and Saluja and Nashine (2012).

scholarly journals Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces

2005 ◽  
Vol 2005 (11) ◽  
pp. 1685-1692 ◽  
Author(s):  
Somyot Plubtieng ◽  
Rabian Wangkeeree
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Convex Subset ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Nonempty Closed Convex Subset ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Completely Continuous

Suppose thatCis a nonempty closed convex subset of a real uniformly convex Banach spaceX. LetT:C→Cbe an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that ifTis uniformlyL-Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point ofT.

scholarly journals The Solution by Iteration of a Composed K-Positive Definite Operator Equation in a Banach Space

2010 ◽  
Vol 2010 ◽  
pp. 1-7
Author(s):  
S. J. Aneke
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Method Of Moments ◽  
Iterative Scheme ◽  
Inverse Function ◽  
Positive Definite ◽  
Inverse Function Theorem ◽  
Definite Operator ◽  
Fréchet Differentiable ◽  
Positive Definite Operator

The equation , where , with being a K-positive definite operator and being a linear operator, is solved in a Banach space. Our scheme provides a generalization to the so-called method of moments studied in a Hilbert space by Petryshyn (1962), as well as Lax and Milgram (1954). Furthermore, an application of the inverse function theorem provides simultaneously a general solution to this equation in some neighborhood of a point , where is Fréchet differentiable and an iterative scheme which converges strongly to the unique solution of this equation.

scholarly journals The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Rabian Wangkeeree ◽  
Pakkapon Preechasilp
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Iterative Methods ◽  
Reflexive Banach Space ◽  
Iterative Scheme ◽  
Duality Mapping ◽  
Nonexpansive Semigroups ◽  
Weakly Continuous ◽  
Asymptotically Nonexpansive ◽  
Weakly Continuous Duality Mapping

We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.

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