scholarly journals On common fixed points, periodic points, and recurrent points of continuous functions

2003 ◽  
Vol 2003 (39) ◽  
pp. 2465-2473 ◽  
Author(s):  
Aliasghar Alikhani-Koopaei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Dense Subset ◽  
Periodic Points ◽  
Continuous Functions ◽  
Common Fixed Points ◽  
Closed Intervals ◽  
Disjoint Sets ◽  
The Common ◽  
Class Of Functions

It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. we had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points. In this paper, we first prove thatSis a nowhere dense subset of[0,1]if and only if{f∈C([0,1]):Fm(f)∩S¯≠∅}is a nowhere dense subset ofC([0,1]). We also give some results about the common fixed, periodic, and recurrent points of functions. We consider the class of functionsfwith continuousωfstudied by Bruckner and Ceder and show that the set of recurrent points of such functions are closed intervals.

scholarly journals On common fixed and periodic points of commuting functions

1998 ◽  
Vol 21 (2) ◽  
pp. 269-276 ◽  
Author(s):  
Aliasghar Alikhani-Koopaei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Periodic Point ◽  
Periodic Points ◽  
Continuous Functions ◽  
Contractive Condition ◽  
Unique Common Fixed Point

It is known that two commuting continuous functions on an interval need not have a common fixed point. It is not known if such two functions have a common periodic point. In this paper we first give some results in this direction. We then define a new contractive condition, under which two continuous functions must have a unique common fixed point.

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 Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Dan Zhang ◽  
Xiaolong Qin ◽  
Feng Gu
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Real Hilbert Space ◽  
Adjoint Operator ◽  
Common Fixed Points ◽  
Nonexpansive Semigroup ◽  
The Common

LetHbe a real Hilbert space. Consider onHa nonexpansive semigroupS={T(s):0≤s<∞}with a common fixed point, a contractionfwith the coefficient0<α<1, and a strongly positive linear bounded self-adjoint operatorAwith the coefficientγ¯>  0. Let0<γ<γ¯/α. It is proved that the sequence{xn}generated by the iterative methodx0∈H, xn+1=αnγf(xn)+βnxn+((1-βn)I-αnA)(1/sn)∫0snT(s)xnds, n≥0converges strongly to a common fixed pointx*∈F(S), whereF(S)denotes the common fixed point of the nonexpansive semigroup. The pointx*solves the variational inequality〈(γf-A)x*,x-x*〉≤0for allx∈F(S).

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>

scholarly journals Common Fixed-Point Theorems in the Partial b -Metric Spaces and an Application to the System of Boundary Value Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Muhammad Nazam ◽  
Zahida Hamid ◽  
Hamed Al Sulami ◽  
Aftab Hussain
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Boundary Value ◽  
Common Fixed Points ◽  
Common Solution ◽  
The Common ◽  
Common Fixed Point Theorems

In this paper, we investigate the conditions for the existence of the common fixed points of generalized contractions in the partial b -metric spaces endowed with an arbitrary binary relation. We establish some unique common fixed-point theorems. The obtained results may generalize and improve earlier fixed-point results. We provide examples to illustrate our findings. As an application, we discuss the common solution to the system of boundary value problems.

scholarly journals Common fixed point theorem on Proinov type mappings via simulation function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Badr Alqahtani ◽  
Sara Salem Alzaid ◽  
Andreea Fulga ◽  
Seher Sultan Yeşilkaya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Simulation Function ◽  
Type Mapping ◽  
The Common ◽  
Common Fixed Point Theorem

AbstractIn this paper, we aim to discuss the common fixed point of Proinov type mapping via simulation function. The presented results not only generalize, but also unify the corresponding results in this direction. We also consider an example to indicate the validity of the obtained results.

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.

scholarly journals Fixed point and a Cantilever beam problem in a partial b-metric space

2021 ◽  
Vol 13 (2) ◽  
pp. 506-518
Author(s):  
Anita Tomar ◽  
Meena Joshi ◽  
Venkatesh Bhatt
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Cantilever Beam ◽  
Metric Space ◽  
Elastic Beam ◽  
The Common ◽  
Type Contraction

Abstract We determine the common fixed point of two maps satisfying Hardy-Roger type contraction in a complete partial b-metric space without exploiting any variant of continuity or commutativity, which is indispensable in analogous results. Towards the end, we give examples and an application to solve a Cantilever beam problem employed in the distortion of an elastic beam in equilibrium to substantiate the utility of these improvements.

scholarly journals Generalized Altering Distances and Common Fixed Points in Ordered Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Common Fixed Points ◽  
Distance Functions ◽  
Ordered Metric Spaces ◽  
System Of Integral Equations ◽  
Common Solution ◽  
Altering Distance

Coincidence point and common fixed point results with the concept of generalized altering distance functions in complete ordered metric spaces are derived. These results generalize the existing fixed point results in the literature. To illustrate our results and to distinguish them from the existing ones, we equip the paper with examples. As an application, we study the existence of a common solution to a system of integral equations.

COMMON FIXED POINT THEOREM FOR TWO MAPPINGS IN bi-b-METRIC SPACE

2022 ◽  
Vol 11 (1) ◽  
pp. 25-34
Author(s):  
V.D. Borgaonkar ◽  
K.L. Bondar ◽  
S.M. Jogdand
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Common ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Unique Common Fixed Point

In this paper we have used the concept of bi-metric space and intoduced the concept of bi-b-metric space. our objective is to obtain the common fixed point theorems for two mappings on two different b-metric spaces induced on same set X. In this paper we prove that on the set X two b-metrics are defined to form two different b-metric spaces and the two mappings defined on X have unique common fixed point.

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