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Tahair Rasham ◽  
Praveen Agarwal ◽  
Laiba Shamshad Abbasi ◽  
Shilpi Jain

2022 ◽  
Vol 2022 ◽  
pp. 1-9
Shazia Kanwal ◽  
Doha Kattan ◽  
Saba Perveen ◽  
Sahidul Islam ◽  
Mohammed Shehu Shagari

In the present research, modern fuzzy technique is used to generalize some conventional and latest results. The objective of this paper is to construct and prove some fixed-point results in complete fuzzy strong b-metric space. Fuzzy strong b-metric (sb-metric) spaces have very useful properties such as openness of open balls whereas it is not held in general for b-metric and fuzzy b-metric spaces. Due to its properties, we have worked in these spaces. In this way, we have generalized some well-known fixed-point theorems in fuzzy version. In addition, some interesting examples are constructed to illustrate our results.

2022 ◽  
Vol 15 ◽  
Guohua Zhou ◽  
Bing Lu ◽  
Xuelong Hu ◽  
Tongguang Ni

Magnetic resonance imaging (MRI) can have a good diagnostic function for important organs and parts of the body. MRI technology has become a common and important disease detection technology. At the same time, medical imaging data is increasing at an explosive rate. Retrieving similar medical images from a huge database is of great significance to doctors’ auxiliary diagnosis and treatment. In this paper, combining the advantages of sparse representation and metric learning, a sparse representation-based discriminative metric learning (SRDML) approach is proposed for medical image retrieval of brain MRI. The SRDML approach uses a sparse representation framework to learn robust feature representation of brain MRI, and uses metric learning to project new features into the metric space with matching discrimination. In such a metric space, the optimal similarity measure is obtained by using the local constraints of atoms and the pairwise constraints of coding coefficients, so that the distance between similar images is less than the given threshold, and the distance between dissimilar images is greater than another given threshold. The experiments are designed and tested on the brain MRI dataset created by Chang. Experimental results show that the SRDML approach can obtain satisfactory retrieval performance and achieve accurate brain MRI image retrieval.

2022 ◽  
Vol 11 (1) ◽  
pp. 25-34
V.D. Borgaonkar ◽  
K.L. Bondar ◽  
S.M. Jogdand

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.

2022 ◽  
Vol 2022 ◽  
pp. 1-8
Aftab Hussain ◽  
Umar Ishtiaq ◽  
Khalil Ahmed ◽  
Hamed Al-Sulami

In this manuscript, we coined pentagonal controlled fuzzy metric spaces and fuzzy controlled hexagonal metric space as generalizations of fuzzy triple controlled metric spaces and fuzzy extended hexagonal b-metric spaces. We use a control function in fuzzy controlled hexagonal metric space and introduce five noncomparable control functions in pentagonal controlled fuzzy metric spaces. In the scenario of pentagonal controlled fuzzy metric spaces, we prove the Banach fixed point theorem, which generalizes the Banach fixed point theorem for the aforementioned spaces. An example is offered to support our main point. We also presented an application to dynamic market equilibrium.

Riya Dutta ◽  
Prasun Kumar Nayak ◽  
Himadri Shekhar Mondal

2022 ◽  
Vol 2022 ◽  
pp. 1-19
Rashad A. R. Bantan ◽  
Saif Ur Rehman ◽  
Shahid Mehmood ◽  
Waleed Almutiry ◽  
Amani Abdullah Alahmadi ◽  

This paper is aimed at establishing some unique common fixed point theorems in complex-valued b -metric space under the rational type contraction conditions for three self-mappings in which the one self-map is continuous. A continuous self-map is commutable with the other two self-mappings. Our results are verified by some suitable examples. Ultimately, our results have been utilized to prove the existing solution to the two Urysohn integral type equations. This application illustrates how complex-valued b -metric space can be used in other types of integral operators.

2022 ◽  
Vol 77 (1) ◽  
Karol Baron ◽  
Rafał Kapica

AbstractAssume $$ (\Omega , {\mathscr {A}}, P) $$ ( Ω , A , P ) is a probability space, X is a compact metric space with the $$ \sigma $$ σ -algebra $$ {\mathscr {B}} $$ B of all its Borel subsets and $$ f: X \times \Omega \rightarrow X $$ f : X × Ω → X is $$ {\mathscr {B}} \otimes {\mathscr {A}} $$ B ⊗ A -measurable and contractive in mean. We consider the sequence of iterates of f defined on $$ X \times \Omega ^{{\mathbb {N}}}$$ X × Ω N by $$f^0(x, \omega ) = x$$ f 0 ( x , ω ) = x and $$ f^n(x, \omega ) = f\big (f^{n-1}(x, \omega ), \omega _n\big )$$ f n ( x , ω ) = f ( f n - 1 ( x , ω ) , ω n ) for $$n \in {\mathbb {N}}$$ n ∈ N , and its weak limit $$\pi $$ π . We show that if $$\psi :X \rightarrow {\mathbb {R}}$$ ψ : X → R is continuous, then for every $$ x \in X $$ x ∈ X the sequence $$\left( \frac{1}{n}\sum _{k=1}^n \psi \big (f^k(x,\cdot )\big )\right) _{n \in {\mathbb {N}}}$$ 1 n ∑ k = 1 n ψ ( f k ( x , · ) ) n ∈ N converges almost surely to $$\int _X\psi d\pi $$ ∫ X ψ d π . In fact, we are focusing on the case where the metric space is complete and separable.

Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman ◽  

A metric space is a set along with a measurement on the set, A metric actuates topological properties like open and shut sets, which lead to the investigation of more theoretical topological spaces. It also has many applications in functional analysis. The aim of this work is design and develop highly efficient algorithms that provide the existence of unique solutions to the differential equation in metric spaces using MATLAB. The quality algorithm was used and developed to solve the differential equation in metric spaces. For accurate results. The proposed model contributed to providing an integrated computer solution for all stages of the solution starting from the stage of solving differential equations in metric space and the stage of displaying and representing the results graphically in the MATLAB program

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