Approximate Fixed Point Sequences of Nonlinear Semigroups in Metric Spaces

2015 ◽  
Vol 58 (2) ◽  
pp. 297-305 ◽  
Author(s):  
M. A. Khamsi
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Ishikawa Iteration ◽  
Nonlinear Semigroups ◽  
Approximate Fixed Point ◽  
Nonexpansive Semigroups ◽  
The Family ◽  
The Common ◽  
Nonlinear Mappings

AbstractIn this paper, we investigate the common approximate fixed point sequences of nonexpansive semigroups of nonlinear mappings {T1}t≥0, i.e., a family such that T0(x) = x, Ts+t = Ts(Tt(x)), where the domain is a metric space (M; d). In particular, we prove that under suitable conditions the common approximate fixed point sequences set is the same as the common approximate fixed point sequences set of two mappings from the family. Then we use the Ishikawa iteration to construct a common approximate fixed point sequence of nonexpansive semigroups of nonlinear mappings.

scholarly journals Approximate Fixed Point Sequences of an Evolution Family on a Metric Space

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Si Fuan ◽  
Rizwan Ullah ◽  
Gul Rahmat ◽  
Muhammad Numan ◽  
Saad Ihsan Butt ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Nonlinear Operator ◽  
Iteration Process ◽  
Evolution Family ◽  
Nonlinear Mapping ◽  
Approximate Fixed Point ◽  
The Family ◽  
Ishikawa Iteration Process ◽  
The Common

In this article, we study the approximate fixed point sequence of an evolution family. A family E=Ux,y;x≥y≥0 of a bounded nonlinear operator acting on a metric space M,d is said to be an evolution family if Ux,x=I and Ux,yUy,z=Ux,z for all x≥y≥z≥0. We prove that the common approximate fixed point sequence is equal to the intersection of the approximate fixed point sequence of two operators from the family. Furthermore, we apply the Ishikawa iteration process to construct an approximate fixed point sequence of an evolution family of nonlinear mapping.

scholarly journals Fixed Point Results for the Family of Multivalued F-Contractive Mappings on Closed Ball in Complete Dislocated b-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 56 ◽  
Author(s):  
Qasim Mahmood ◽  
Abdullah Shoaib ◽  
Tahair Rasham ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
System Of Integral Equations ◽  
Contractive Mappings ◽  
The Family ◽  
Rational Type

The purpose of this paper is to find out fixed point results for the family of multivalued mappings fulfilling a generalized rational type F-contractive conditions on a closed ball in complete dislocated b-metric space. An application to the system of integral equations is presented to show the novelty of our results. Our results extend several comparable results in the existing literature.

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.

scholarly journals Approximation fixed theorems for α-partial weakly Zamfirescu mappings with application to homotopy invariance

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1941-1956
Author(s):  
Aphinat Ninsri ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Binary Relation ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Homotopy Invariance ◽  
Complete Metric Spaces ◽  
Approximate Fixed Point

In this paper, we introduce the concept of ?-partial weakly Zamfirescu mappings and give some approximate fixed point results for this mapping in ?-complete metric spaces. We also give some approximate fixed point results in ?-complete metric space endowed with an arbitrary binary relation and approximate fixed point results in ?-complete metric space endowed with graph. As application, we give homotopy results for ?-partial weakly Zamfirescu mapping.

scholarly journals On Multivalued Contractions in Cone Metric Spaces without Normality

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Muhammad Arshad ◽  
Jamshaid Ahmad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Normal Cone ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Cone Metric Spaces ◽  
The Family ◽  
Multivalued Contractions ◽  
Cone Metric

Wardowski (2011) in this paper for a normal cone metric space(X,d)and for the family𝒜of subsets ofXestablished a new cone metricH:𝒜×𝒜→Eand obtained fixed point of set-valued contraction of Nadler type. Further, it is noticed in the work of Janković et al., 2011 that the…fixed-point problem in the setting of cone metric spaces is appropriate only in the case when the underlying cone is nonnormal. In the present paper we improve Wardowski's result by proving the same without the assumption of normality on cones.

scholarly journals On Multivalued Fuzzy Contractions in Extended b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Nayab Alamgir ◽  
Quanita Kiran ◽  
Hassen Aydi ◽  
Yaé Ulrich Gaba
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Contraction Mappings ◽  
Nadler’S Fixed Point Theorem ◽  
The Family ◽  
Fuzzy Fixed Point

In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b -metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α -fuzzy fixed point theorems in the context of extended b -metric spaces that generalize Nadler’s fixed point theorem as well as many preexisting results in the literature. Further, we establish α -fuzzy fixed point theorems for Ćirić type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results.

scholarly journals Approximations of Fixed Points in the Hadamard Metric Space CATp(0)

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1088
Author(s):  
Mostafa Bachar ◽  
Mohamed Amine Khamsi
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Metric Space ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Approximate Fixed Point ◽  
Successive Iteration ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

In this paper, we consider the recently introduced C A T p ( 0 ) , where the comparison triangles belong to ℓ p , for p ≥ 2 . We first establish an inequality in these nonlinear metric spaces. Then, we use it to prove the existence of fixed points of asymptotically nonexpansive mappings defined in C A T p ( 0 ) . Moreover, we discuss the behavior of the successive iteration introduced by Schu for these mappings in Banach spaces. In particular, we prove that the successive iteration generates an approximate fixed point sequence.

scholarly journals A general lemma for fixed-point theorems involving more than two maps inD-metric spaces with applications

2003 ◽  
Vol 2003 (11) ◽  
pp. 661-672
Author(s):  
B. C. Dhage ◽  
Smrati Arya ◽  
Jeong Sheok Ume
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
General Lemma ◽  
The Common ◽  
Common Fixed Point Theorems

A general procedural lemma for fixed-point theorems for three and four maps in aD-metric space is proved, and it is further applied for proving the common fixed-point theorems of three and four maps in aD-metric space satisfying certain contractive conditions.

scholarly journals COMMUNAL FIXED POINT IN FUZZY 2- METRIC SPACES

2021 ◽  
Vol 7 (7) ◽  
pp. 481-487
Author(s):  
Atianashie Miracle A ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Compatible Mappings ◽  
The Common ◽  
Common Fixed Point Theorem

The objective of this paper is to emphasize the Common Fixed Point in Fuzzy 2- Metric Spaces and prove a common fixed point theorem of compatible mappings of type (R) in fuzzy 2-metric space. We consider four mappings of which one is continuous. The results generalize many results in the literature. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and the degree of utility of our results.

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.

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