scholarly journals Some fixed point iteration procedures

1991 ◽  
Vol 14 (1) ◽  
pp. 1-16 ◽  
Author(s):  
B. E. Rhoades
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Complete Coverage ◽  
Fixed Point Iteration

This paper provides a survey of iteration procedures that have been used to obtain fixed points for maps satisfying a variety of contractive conditions. The author does not claim to provide complete coverage of the literature, and admits to certain biases in the theorems that are cited herein. In spite of these shortcomings, however, this paper should be a useful reference for those persons wishing to become better acquainted with the area.

scholarly journals Geometrically Constructed Family of the Simple Fixed Point Iteration Method

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 694
Author(s):  
Vinay Kanwar ◽  
Puneet Sharma ◽  
Ioannis K. Argyros ◽  
Ramandeep Behl ◽  
Christopher Argyros ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Nonlinear Equations ◽  
Iteration Method ◽  
Parameter Family ◽  
Arbitrary Parameter ◽  
Fixed Point Iteration ◽  
Iterative Schemes ◽  
Straight Line ◽  
Predictor Corrector

This study presents a new one-parameter family of the well-known fixed point iteration method for solving nonlinear equations numerically. The proposed family is derived by implementing approximation through a straight line. The presence of an arbitrary parameter in the proposed family improves convergence characteristic of the simple fixed point iteration as it has a wider domain of convergence. Furthermore, we propose many two-step predictor–corrector iterative schemes for finding fixed points, which inherit the advantages of the proposed fixed point iterative schemes. Finally, several examples are given to further illustrate their efficiency.

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 A comparison of some fixed point iteration procedures by using the basins of attraction

2016 ◽  
Vol 32 (3) ◽  
pp. 277-284
Author(s):  
GHEORGHE ARDELEAN ◽  
◽  
OVIDIU COSMA ◽  
LASZLO BALOG ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Basins Of Attraction ◽  
Numerical Results ◽  
Complex Polynomials ◽  
Empirical Comparison ◽  
Fixed Point Iteration ◽  
Newton's Iteration ◽  
Iterative Processes ◽  
Points Approximation

Several iterative processes have been defined by researchers to approximate the fixed points of various classes operators. In this paper we present, by using the basins of attraction for the roots of some complex polynomials, an empirical comparison of some iteration procedures for fixed points approximation of Newton’s iteration operator. Some numerical results are presented. The Matlab m-files for generating the basins of attraction are presented, too.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

Coincidence and fixed points for hybrid tangential maps

2010 ◽  
Vol 17 (2) ◽  
pp. 273-285
Author(s):  
Tayyab Kamran ◽  
Quanita Kiran
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Property ◽  
Fixed Point Theorems ◽  
Acta Math ◽  
Contractive Condition ◽  
The Common

Abstract In [Int. J. Math. Math. Sci. 2005: 3045–3055] by Liu et al. the common property (E.A) for two pairs of hybrid maps is defined. Recently, O'Regan and Shahzad [Acta Math. Sin. (Engl. Ser.) 23: 1601–1610, 2007] have introduced a very general contractive condition and obtained some fixed point results for hybrid maps. We introduce a new property for pairs of hybrid maps that contains the property (E.A) and obtain some coincidence and fixed point theorems that extend/generalize some results from the above-mentioned papers.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

scholarly journals Differentiable Forward and Backward Fixed-Point Iteration Layers

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 18383-18392
Author(s):  
Younghan Jeon ◽  
Minsik Lee ◽  
Jin Young Choi
Keyword(s):  
Fixed Point ◽  
Fixed Point Iteration

scholarly journals CONFORMAL HOUSE

2010 ◽  
Vol 25 (24) ◽  
pp. 4603-4621 ◽  
Author(s):  
THOMAS A. RYTTOV ◽  
FRANCESCO SANNINO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Gauge Group ◽  
Gauge Theories ◽  
Simultaneous Presence ◽  
Consistency Check ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Mass Terms

We investigate the gauge dynamics of nonsupersymmetric SU (N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

scholarly journals Common fixed points of single-valued and multivalued maps

2005 ◽  
Vol 2005 (19) ◽  
pp. 3045-3055 ◽  
Author(s):  
Yicheng Liu ◽  
Jun Wu ◽  
Zhixiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Common Fixed Points ◽  
Partial Answer ◽  
Multivalued Maps ◽  
Hybrid Pair ◽  
Common Fixed Point Theorems

We define a new property which contains the property (EA) for a hybrid pair of single- and multivalued maps and give some new common fixed point theorems under hybrid contractive conditions. Our results extend previous ones. As an application, we give a partial answer to the problem raised by Singh and Mishra.

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