scholarly journals Fixed Point Results for Rational Orbitally ( Θ , δ b )-Contractions with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhenhua Ma ◽  
Jamshaid Ahmad ◽  
Abdullah Eqal Al-Mazrooei ◽  
Durdana Lateef
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Integral Inclusion

The purpose of this paper is to define a rational orbitally ( Θ , δ b )-contraction and prove some new results in the context of b -metric spaces. Our results extend, generalize, and unify some known results in the literature. As application of our main result, we investigate the solution of Fredholm integral inclusion. We also provide an example to substantiate the advantage and usefulness of obtained results.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion

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 A Solution of Fredholm Integral Inclusions via Suzuki-Type Fuzzy Contractions

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Izhar Uddin ◽  
Atiya Perveen ◽  
Hüseyin Işık ◽  
Ramakant Bhardwaj
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Existence Of A Solution ◽  
Integral Inclusion ◽  
Fuzzy Fixed Point

In this study, we introduce fuzzy weak ϕ -contraction and Suzuki-type fuzzy weak ϕ -contraction and employ these to prove some fuzzy fixed point results for fuzzy mappings in the setting of metric spaces, which is followed by an example to support our claim. Next, we deduce some corollaries and fixed point results for multivalued mappings from our main result. Finally, as an application of our result, we provide the existence of a solution for a Fredholm integral inclusion.

scholarly journals Solutions to Fredholm Integral Inclusions via Generalized Fuzzy Contractions

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 808 ◽  
Author(s):  
Hamed H Al-Sulami ◽  
Jamshaid Ahmad ◽  
Nawab Hussain ◽  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Unknown Function ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Multivalued Operator ◽  
Complete Metric Spaces ◽  
New Class ◽  
Integral Inclusion ◽  
The Family

The aim of this study is to investigate the existence of solutions for the following Fredholm integral inclusion φ ( t ) ∈ f ( t ) + ∫ 0 1 K ( t , s , φ ( s ) ) ϱ s for t ∈ [ 0 , 1 ] , where f ∈ C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] × [ 0 , 1 ] × R → K c v ( R ) a given multivalued operator, where K c v represents the family of non-empty compact and convex subsets of R , φ ∈ C [ 0 , 1 ] is the unknown function and ϱ is a metric defined on C [ 0 , 1 ] . To attain this target, we take advantage of fixed point theorems for α -fuzzy mappings satisfying a new class of contractive conditions in the context of complete metric spaces. We derive new fixed point results which extend and improve the well-known results of Banach, Kannan, Chatterjea, Reich, Hardy-Rogers, Berinde and Ćirić by means of this new class of contractions. We also give a significantly non-trivial example to support our new results.

scholarly journals Solution to Fredholm integral inclusions via (F, δb)-contractions

2016 ◽  
Vol 14 (1) ◽  
pp. 1053-1064 ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Ravi P. Agarwal ◽  
Zoran Kadelburg
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Integral Inclusion

AbstractWe present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.

scholarly journals Set-Valued SU-Type Fixed Point Theorems via Gauge Function with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Amjad Ali ◽  
Monairah Alansari Rather ◽  
Fahim Uddin ◽  
Muhammad Arshad ◽  
Awais Asif ◽  
...  
Keyword(s):  
Dynamical System ◽  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Gauge Function ◽  
Integral Inclusion

In this article, we have designed two existence of fixed point theorems which are regarding to set-valued SU-type θ η -contraction and Γ α -contraction via gauge function in the setting of metric spaces. An extensive set of nontrivial example will be given to justify our claim. At the end, we will give an application to prove the existence behavior for the system of functional equation in dynamical system and integral inclusion.

Common Fixed Point Results for Three Maps in Cone Metric Spaces

2014 ◽  
Vol 1 (3) ◽  
pp. 42-47
Author(s):  
K. Prudhvi ◽  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Cone Metric Spaces ◽  
Cone Metric

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

Some Fixed Point Theorems in G � Metric Spaces

2019 ◽  
Vol 10 (1) ◽  
pp. 151-158
Author(s):  
Bijay Kumar Singh ◽  
Pradeep Kumar Pathak
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces
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