scholarly journals Higher Order of Convergence with Multivalued Contraction Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jia-Bao Liu ◽  
Asma Rashid Butt ◽  
Shahzad Nadeem ◽  
Shahbaz Ali ◽  
Muhammad Shoaib
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Order Of Convergence ◽  
Higher Order ◽  
Gauge Function ◽  
Multivalued Mappings ◽  
Contraction Mappings ◽  
Multivalued Contraction ◽  
Integral Inclusion

In this paper, we establish some theorems of fixed point on multivalued mappings satisfying contraction mapping by using gauge function. Furthermore, we use Q - and R -order of convergence. Our main results extend many previous existing results in the literature. Consequently, to substantiate the validity of proposed method, we give its application in integral inclusion.

scholarly journals Multivalued weak cyclic δ-contraction mappings

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pulak Konar ◽  
Samir Kumar Bhandari ◽  
Sumit Chandok ◽  
Aiman Mukheimer
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Cyclic Contraction ◽  
Contraction Mappings ◽  
Multivalued Contraction ◽  
New Type

AbstractIn this paper, we propose some new type of weak cyclic multivalued contraction mappings by generalizing the cyclic contraction using the δ-distance function. Several novel fixed point results are deduced for such class of weak cyclic multivalued mappings in the framework of metric spaces. Also, we construct some examples to validate the usability of the results. Various existing results of the literature are generalized.

scholarly journals Multivalued contraction maps on fuzzy $ b $-metric spaces and an application

2022 ◽  
Vol 7 (4) ◽  
pp. 5925-5942
Author(s):  
Samina Batul ◽  
◽  
Faisar Mehmood ◽  
Azhar Hussain ◽  
Dur-e-Shehwar Sagheer ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Existence Of A Solution ◽  
Multivalued Contraction ◽  
Integral Inclusion ◽  
Special Cases ◽  
Contraction Maps

<abstract><p>In this article, the concept of a Hausdorff fuzzy $ b $-metric space is introduced. The new notion is used to establish some fixed point results for multivalued mappings in $ G $-complete fuzzy $ b $-metric spaces satisfying a suitable requirement of contractiveness. An illustrative example is formulated to support the results. Eventually, an application for the existence of a solution for an integral inclusion is established which involves showing the materiality of the obtained results. These results are more general and some theorems proved by of Shehzad et al. are their special cases.</p></abstract>

scholarly journals Multivalued φ contractions and fixed point theorems

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1209-1220 ◽  
Author(s):  
Maria Samreen ◽  
Khansa Waheed ◽  
Quanita Kiran
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Primary Structure ◽  
Existence Result ◽  
Fixed Point Theorems ◽  
Iterative Scheme ◽  
Higher Order ◽  
Multivalued Mappings ◽  
Contractive Condition ◽  
Integral Inclusion

In this paper we establish some fixed point theorems for multivalued mappings satisfying contractive condition involving gauge function when the underlying primary structure is b-metric space. Our proposed iterative scheme converges to the fixed point with higher order. Moreover, we also calculate priori and posteriori estimates for the fixed point. Our main results generalize/extend many perexisting results in literature. Consequently, to substantiate the validity of our result we obtain an existence result for the solution of integral inclusion.

scholarly journals New Fixed Point Results via a Graph Structure

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1013
Author(s):  
Özlem Acar ◽  
Hassen Aydi ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Graph Structure ◽  
Contraction Mappings ◽  
Multivalued Contraction

The main aim of this paper is to introduce and study some fixed point results for rational multivalued G-contraction and F-Khan-type multivalued contraction mappings on a metric space with a graph. At the end, we give an illustrative example.

Best approximation and fixed points for rational-type contraction mappings

2019 ◽  
Vol 25 (2) ◽  
pp. 205-209
Author(s):  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Best Approximation ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Invariant Approximation ◽  
Frame Work ◽  
Rational Type ◽  
Type Contraction

AbstractIn this paper, we prove a fixed point theorem for a rational type contraction mapping in the frame work of metric spaces. Also, we extend Brosowski–Meinardus type results on invariant approximation for such class of contraction mappings. The results proved extend some of the known results existing in the literature.

scholarly journals An Iteration Scheme for Contraction Mappings with an Application to Synchronization of Discrete Logistic Maps

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Ke Ding ◽  
Jong Kyu Kim ◽  
Qiang Lu ◽  
Bin Du
Keyword(s):  
Fixed Point ◽  
Convergence Rate ◽  
Contraction Mapping ◽  
Nonexpansive Mappings ◽  
Positive Influence ◽  
Iteration Scheme ◽  
Contraction Mappings ◽  
Iterative Schemes ◽  
Comparison Results ◽  
The Given

This paper deals with designing a new iteration scheme associated with a given scheme for contraction mappings. This new scheme has a similar structure to that of the given scheme, in which those two iterative schemes converge to the same fixed point of the given contraction mapping. The positive influence of feedback parameters on the convergence rate of this new scheme is investigated. Moreover, the derived convergence and comparison results can be extended to nonexpansive mappings. As an application, the derived results are utilized to study the synchronization of logistic maps. Two illustrated examples are used to reveal the effectiveness of our results.

scholarly journals Some best proximity point results for multivalued mappings on partial metric spaces

2021 ◽  
Vol 25 (1) ◽  
pp. 99-111
Author(s):  
Mustafa Aslantas ◽  
Al-Zuhairi Abed
Keyword(s):  
Contraction Mapping ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Multivalued Mappings ◽  
Partial Metric ◽  
Multivalued Contraction ◽  
New Concepts ◽  
Partial Metric Spaces

In this paper, we introduce two new concepts of Feng-Liu type multivalued contraction mapping and cyclic Feng-Liu type multivalued contraction mapping. Then, we obtain some new best proximity point results for such mappings on partial metric spaces by considering Feng-Liu's technique. Finally, we provide examples to show the effectiveness of our results.

Stability results for fixed point sets of α*- Ψ contractive multivalued mappings

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3665-3670
Author(s):  
Binayak Choudhury ◽  
Chaitali Bandyopadhyay ◽  
Rajendra Pant
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Stability Result ◽  
Multivalued Mappings ◽  
Point Sets ◽  
Generalized Contraction ◽  
Class Of Functions ◽  
Stability Results ◽  
Fixed Point Sets

In this paper, we established a stability result for fixed point sets associated with a sequence of multivalued mappings which belong to class of functions obtained by a multivalued extension of certain generalized contraction mapping. Certain other aspects of these mappings are already studied in the existing literatures. We also construct an illustrative example.

scholarly journals Related Results to Hybrid Pair of Mappings and Applications in Bipolar Metric Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
G. N. V. Kishore ◽  
K. P. R. Rao ◽  
A. Sombabu ◽  
R. V. N. S. Rao
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Contractive Mapping ◽  
Mixed Monotone Property ◽  
Contraction Mappings ◽  
Monotone Property ◽  
Partially Ordered ◽  
Multivalued Contraction ◽  
Hybrid Pair

In this paper, we introduce the concept of multivalued contraction mappings in partially ordered bipolar metric spaces and establish the existence of unique coupled fixed point results for multivalued contractive mapping by using mixed monotone property in partially ordered bipolar metric spaces. Some interesting consequences of our results are obtained.

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