scholarly journals Equivalence results for implicit Jungck–Kirk type iterations

2018 ◽  
Vol 22 (1) ◽  
pp. 75-89
Author(s):  
H. Akewe ◽  
A. A. Mogbademu
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Points ◽  
Fixed Point Iteration ◽  
Linear Spaces ◽  
Mann Iteration ◽  
Normed Linear Spaces ◽  
Weakly Compatible ◽  
The Common

We show that the implicit Jungck–Kirk-multistep, implicit Jungck–Kirk–Noor, implicit Jungck–Kirk–Ishikawa, and implicit Jungck–Kirk–Mann iteration schemes are equivalently used to approximate the common fixed points of a pair of weakly compatible generalized contractive-like operators defined on normed linear spaces. Our results contribute to the existing results on the equivalence of fixed point iteration schemes by extending them to pairs of maps. An example to show the applicability of the main results is included.

scholarly journals On Multistep Iterative Scheme for Approximating the Common Fixed Points of Contractive-Like Operators

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
J. O. Olaleru ◽  
H. Akewe
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Weakly Compatible ◽  
The Common ◽  
Unique Common Fixed Point

We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa, and Jungck-Noor iterations can also be used to approximate the common fixed points of such maps. The results are improvements, generalizations, and extensions of the work of Olatinwo and Imoru (2008), Olatinwo (2008). Consequently, several results in literature are generalized.

scholarly journals Coincidence and fixed points for compatible and relatively nonexpansive maps

1993 ◽  
Vol 16 (1) ◽  
pp. 95-100 ◽  
Author(s):  
Gerald Jungck
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Nonexpansive Maps ◽  
Relatively Nonexpansive ◽  
Compact Subsets

The concept of relatively nonexpansive maps is introduced. Fixed point and coincidence results for families of four self maps of metric spaces are obtained. Non-continuous compatible and relatively nonexpansive maps on star-shaped compact subsets of normed linear spaces are highlighted, and two theorems of Dotson are generalized.

scholarly journals Common fixed points under contractive conditions of integral type

2020 ◽  
Vol 28 (1) ◽  
pp. 41-57
Author(s):  
Hakima Bouhadjera
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Common Fixed Points ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Integral Type ◽  
Weakly Compatible ◽  
Common Fixed Point Theorems

AbstractIn this paper, we give some common fixed point theorems for a class of occasionally weakly compatible mappings satisfying contractive conditions of integral type. Our results generalize a host of previously theorems. We also present some illustrative examples which support our main results and show the applicability and validity of these results.

scholarly journals Iterative Schemes for Fixed Point Computation of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Rudong Chen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Minimum Norm ◽  
Practical Applications ◽  
Fixed Point Computation ◽  
The Common ◽  
Special Case

Fixed point (especially, the minimum norm fixed point) computation is an interesting topic due to its practical applications in natural science. The purpose of the paper is devoted to finding the common fixed points of an infinite family of nonexpansive mappings. We introduce an iterative algorithm and prove that suggested scheme converges strongly to the common fixed points of an infinite family of nonexpansive mappings under some mild conditions. As a special case, we can find the minimum norm common fixed point of an infinite family of nonexpansive mappings.

scholarly journals On Fixed Points of Asymptotically Regular Mappings

1987 ◽  
Vol 43 (3) ◽  
pp. 328-346 ◽  
Author(s):  
B. E. Rhoades ◽  
S. sessa ◽  
M. S. Khan ◽  
M. Swaleh
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Linear Spaces ◽  
Complete Metric Spaces ◽  
Normed Linear Spaces ◽  
Asymptotically Regular

Some results on fixed points of asymptotically regular mappings are obtained in complete metric spaces and normed linear spaces.The structure of the set of common fixed points is also discussed in Banach spaces. Our work generalizes essentially known results of Das and Naik, Fisher, Jaggi, Jungck, Rhoades, Singh and Tiwari and several others.

scholarly journals Viscosity Method for Hierarchical Fixed Point Problems with an Infinite Family of Nonexpansive Nonself-Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yaqin Wang
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Fixed Points ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Fixed Point Problems ◽  
Viscosity Method ◽  
Hierarchical Fixed Point ◽  
The Common ◽  
Hierarchical Fixed Point Problems

A viscosity method for hierarchical fixed point problems is presented to solve variational inequalities, where the involved mappings are nonexpansive nonself-mappings. Solutions are sought in the set of the common fixed points of an infinite family of nonexpansive nonself-mappings. The results generalize and improve the recent results announced by many other authors.

scholarly journals Retraction method in fixed point theory for monotone nonexpansive mappings

2016 ◽  
Vol 32 (3) ◽  
pp. 271-276
Author(s):  
M. R. ALFURAIDAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Common Fixed Points ◽  
The Common ◽  
Nonexpansive Retract

In this paper we study the properties of the common fixed points set of a commuting family of monotone nonexpansive mappings in Banach spaces endowed with a graph. In particular, we prove that under certain conditions, this set is a monotone nonexpansive retract.

Common fixed point of Jungck-Kirk-type iterations for non-self operators in normed linear spaces

2016 ◽  
Vol 56 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Hudson Akewe ◽  
Adesanmi Mogbademu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Linear Space ◽  
Normed Linear Space ◽  
Linear Spaces ◽  
Iterative Schemes ◽  
Normed Linear Spaces ◽  
The Common ◽  
Stability Results

Abstract In this paper, we introduce Jungck-Kirk-multistep and Jungck-Kirk-multistep-SP iterative schemes and use their strong convergences to approximate the common fixed point of nonself operators in a normed linear Space. The Jungck-Kirk-Noor, Jungck-Kirk-SP, Jungck-Kirk-Ishikawa, Jungck-Kirk-Mann and Jungck-Kirk iterative schemes follow our results as corollaries. We also study and prove stability results of these schemes in a normed linear space. Our results generalize and unify most approximation and stability results in the literature.

scholarly journals A Common Coincidence of Fixed Point for Generalized Caristi Fixed Point Theorem

2021 ◽  
Vol 2 (1) ◽  
pp. 40-46
Author(s):  
Jayashree Patil ◽  
Basel Hardan ◽  
Amol Bachhav
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Common Fixed Points ◽  
Weakly Compatible

In this paper, the interpolative Caristi type weakly compatible contractive in a complete metric space is applied to show some common fixed points results related to such mappings. Our application shows that the function which is used to prove the obtained results is a bounded map. An example is provided to show the useability of the acquired results.

scholarly journals Approximation of common fixed points in 2-Banach spaces with applications

2019 ◽  
Vol 20 (1) ◽  
pp. 43
Author(s):  
D. Ramesh Kumar ◽  
M. Pitchaimani
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Contractive Condition ◽  
Common Fixed Point Problem ◽  
The Common

<p>The purpose of this paper is to establish the existence and uniqueness of common fixed points of a family of self-mappings satisfying generalized rational contractive condition in 2-Banach spaces. An example is included to justify our results. We approximate the common fixed point by Mann and Picard type iteration schemes. Further, an application to well-posedness of the common fixed point problem is given. The presented results generalize many known results on 2-Banach spaces.</p>

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