An Iterative Scheme for the Approximations of Fixed Points of Asymptotically Pseudocontractive Mappings

2011 ◽  
Vol 32 (3) ◽  
pp. 342-350
Author(s):  
Arif Rafiq
Keyword(s):  
Fixed Points ◽  
Iterative Scheme ◽  
Pseudocontractive Mappings ◽  
Asymptotically Pseudocontractive Mappings

scholarly journals Fixed point iterations of three asymptotically pseudocontractive mappings

2013 ◽  
Vol 46 (3) ◽  
Author(s):  
Arif Rafiq
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Independent Interest ◽  
Pseudocontractive Mappings ◽  
Asymptotically Pseudocontractive Mappings ◽  
Fixed Point Iterations

AbstractIn this paper, we establish the strong convergence for a modified three-step iterative scheme with errors associated with three mappings in real Banach spaces. Moreover, our technique of proofs is of independent interest. Remark at the end simplifies many known results.

scholarly journals On the Convergence of Implicit Iterative Processes for Asymptotically Pseudocontractive Mappings in the Intermediate Sense

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Xiaolong Qin ◽  
Jong Kyu Kim ◽  
Tianze Wang
Keyword(s):  
Hilbert Space ◽  
Weak Convergence ◽  
Fixed Points ◽  
Iterative Process ◽  
Real Hilbert Space ◽  
Common Fixed Points ◽  
Finite Family ◽  
Strong And Weak Convergence ◽  
Pseudocontractive Mappings ◽  
Asymptotically Pseudocontractive Mappings

An implicit iterative process is considered. Strong and weak convergence theorems of common fixed points of a finite family of asymptotically pseudocontractive mappings in the intermediate sense are established in a real Hilbert space.

A modified Krasnosellkii-Mann algorithms for computing fixed points of multivalued quasi-nonexpansive mappings in Banach spaces

2019 ◽  
Vol 28 (2) ◽  
pp. 191-198
Author(s):  
T. M. M. SOW
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Mann Iteration ◽  
Infinite Dimensional ◽  
Mann Algorithm

It is well known that Krasnoselskii-Mann iteration of nonexpansive mappings find application in many areas of mathematics and know to be weakly convergent in the infinite dimensional setting. In this paper, we introduce and study an explicit iterative scheme by a modified Krasnoselskii-Mann algorithm for approximating fixed points of multivalued quasi-nonexpansive mappings in Banach spaces. Strong convergence of the sequence generated by this algorithm is established. There is no compactness assumption. The results obtained in this paper are significant improvement on important recent results.

Explicit algorithms for J-fixed points of some non linear mappings in certain Banach spaces

2020 ◽  
Vol 29 (1) ◽  
pp. 27-36
Author(s):  
M. M. GUEYE ◽  
M. SENE ◽  
M. NDIAYE ◽  
N. DJITTE
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Maximal Monotone ◽  
Point Theory ◽  
Duality Mapping ◽  
Monotone Mappings ◽  
Normalized Duality Mapping ◽  
Maximal Monotone Mappings ◽  
Pseudocontractive Mappings

Let E be a real normed linear space and E∗ its dual. In a recent work, Chidume et al. [Chidume, C. E. and Idu, K. O., Approximation of zeros of bounded maximal monotone mappings, solutions of hammerstein integral equations and convex minimizations problems, Fixed Point Theory and Applications, 97 (2016)] introduced the new concepts of J-fixed points and J-pseudocontractive mappings and they shown that a mapping A : E → 2 E∗ is monotone if and only if the map T := (J −A) : E → 2 E∗ is J-pseudocontractive, where J is the normalized duality mapping of E. It is our purpose in this work to introduce an algorithm for approximating J-fixed points of J-pseudocontractive mappings. Our results are applied to approximate zeros of monotone mappings in certain Banach spaces. The results obtained here, extend and unify some recent results in this direction for the class of maximal monotone mappings in uniformly smooth and strictly convex real Banach spaces. Our proof is of independent interest.

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.

scholarly journals Convergence and Stability Results of Modified CUIA Iterative Scheme for Hyperbolic Convex Metric space

2021 ◽  
Vol 2089 (1) ◽  
pp. 012040
Author(s):  
Surjeet Singh Chauhan Gonder ◽  
Khushboo Basra
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Metric Space ◽  
Iterative Scheme ◽  
Real Life ◽  
Convex Metric Space ◽  
Convergence And Stability ◽  
Life Problems ◽  
Stability Results ◽  
Differential And Integral Equations

Abstract The iterative fixed points have numerous applications in locating the solution of some real-life problems which can be modelled into linear as well as nonlinear differential and integral equations. In this manuscript, first of all, a new iterative scheme namely Modified CUIA iterative scheme is introduced. We first prove a theorem to check the convergence of this iteration for Hyperbolic Convex metric space. The result is then supported with one example. Further, another theorem is proved establishing the weak T stability of modified CUIA iterative scheme on the above space.

scholarly journals A Modified Mixed Ishikawa Iteration for Common Fixed Points of Two Asymptotically Quasi Pseudocontractive Type Non-Self-Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yuanheng Wang ◽  
Huimin Shi
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Iterative Sequence ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
Ishikawa Iterative Sequence

A new modified mixed Ishikawa iterative sequence with error for common fixed points of two asymptotically quasi pseudocontractive type non-self-mappings is introduced. By the flexible use of the iterative scheme and a new lemma, some strong convergence theorems are proved under suitable conditions. The results in this paper improve and generalize some existing results.

Sign in / Sign up

Export Citation Format

Share Document