integral inclusion
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2022 ◽  
Vol 7 (4) ◽  
pp. 5925-5942
Author(s):  
Samina Batul ◽  
◽  
Faisar Mehmood ◽  
Azhar Hussain ◽  
Dur-e-Shehwar Sagheer ◽  
...  

<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>


Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1927
Author(s):  
Fatemeh Lael ◽  
Naeem Saleem ◽  
Liliana Guran ◽  
Monica Felicia Bota

This manuscript is focused on the role of convexity of the modular, and some fixed point results for contractive correspondence and single-valued mappings are presented. Further, we prove Nadler’s Theorem and some fixed point results on orthogonal modular spaces. We present an application to a particular form of integral inclusion to support our proposed version of Nadler’s theorem.


2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhenhua Ma ◽  
Jamshaid Ahmad ◽  
Abdullah Eqal Al-Mazrooei ◽  
Durdana Lateef

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.


2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Izhar Uddin ◽  
Atiya Perveen ◽  
Hüseyin Işık ◽  
Ramakant Bhardwaj

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.


2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Amjad Ali ◽  
Monairah Alansari Rather ◽  
Fahim Uddin ◽  
Muhammad Arshad ◽  
Awais Asif ◽  
...  

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.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed El-Sayed ◽  
Shorouk Al-Issa ◽  
Yasmin Omar

AbstractWe investigate the existence of solutions for a nonlinear integral inclusion of Urysohn–Stieltjes type. As applications, we give a Chandrasekhar quadratic integral equation and a nonlinear Chandrasekhar integral inclusion.


Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12
Author(s):  
Reny George ◽  
Hemanth Kumar Pathak

The Hβ-Hausdorff–Pompeiu b-metric for β∈[0,1] is introduced as a new variant of the Hausdorff–Pompeiu b-metric H. Various types of multi-valued Hβ-contractions are introduced and fixed point theorems are proved for such contractions in a b-metric space. The multi-valued Nadler contraction, Czervik contraction, q-quasi contraction, Hardy Rogers contraction, weak quasi contraction and Ciric contraction existing in literature are all one or the other type of multi-valued Hβ-contraction but the converse is not necessarily true. Proper examples are given in support of our claim. As applications of our results, we have proved the existence of a unique multi-valued fractal of an iterated multifunction system defined on a b-metric space and an existence theorem of Filippov type for an integral inclusion problem by introducing a generalized norm on the space of selections of the multifunction.


2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jia-Bao Liu ◽  
Asma Rashid Butt ◽  
Shahzad Nadeem ◽  
Shahbaz Ali ◽  
Muhammad Shoaib

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.


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