scholarly journals Some geometric properties in modular spaces and application to fixed point theory

2004 ◽  
Vol 295 (2) ◽  
pp. 576-594 ◽  
Author(s):  
Maria A Japón
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Geometric Properties ◽  
Modular Spaces

scholarly journals On the Generalized Ulam-Hyers-Rassias Stability of Quadratic Mappings in Modular Spaces withoutΔ2-Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Kittipong Wongkum ◽  
Parin Chaipunya ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Lower Semicontinuous ◽  
Point Theory ◽  
Quadratic Functional ◽  
Modular Spaces ◽  
Quadratic Mappings ◽  
Rassias Stability

We approach the generalized Ulam-Hyers-Rassias (briefly, UHR) stability of quadratic functional equations via the extensive studies of fixed point theory. Our results are obtained in the framework of modular spaces whose modulars are lower semicontinuous (briefly, lsc) but do not satisfy any relatives ofΔ2-conditions.

scholarly journals Fixed points results in modular vector spaces with applications to quantum operations and Markov operators

2020 ◽  
Vol 36 (2) ◽  
pp. 277-286
Author(s):  
MOHAMED AMINE KHAMSI ◽  
◽  
POOM KUMAM ◽  
UMAR BATSARI YUSUF ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Order Relation ◽  
Modular Function ◽  
Point Theory ◽  
Function Spaces ◽  
Vector Spaces ◽  
Markov Operators ◽  
Modular Spaces ◽  
Modular Function Spaces

Recently, researchers are showing more interest on both modular vector spaces and modular function spaces. Looking at the number of results it is pertinent to say that, exploration in this direction especially in the area of fixed point theory and applications is still ongoing, many good results can still be unveiled. As a contribution from our part, we study some fixed point results in modular vector spaces associated with order relation. As an application, we were able to study the existence of fixed point(s) of both depolarizing quantum operation and Markov operators through modular functions/modular spaces. The awareness on the importance of quantum theory and Economics globally were the sole motivations of the application choices in our work. Our work complement the existing results. In fact, it adds to the number of application areas that modular vector/function spaces covered.

scholarly journals Convexity and boundedness relaxation for fixed point theorems in modular spaces

2021 ◽  
Vol 22 (1) ◽  
pp. 91
Author(s):  
Fatemeh Lael ◽  
Samira Shabanian
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Recent Trend ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Vector Spaces ◽  
Modular Spaces ◽  
Mathematical Problems ◽  
Normed Vector

<p>Although fixed point theorems in modular spaces have remarkably applied to a wide variety of mathematical problems, these theorems strongly depend on some assumptions which often do not hold in practice or can lead to their reformulations as particular problems in normed vector spaces. A recent trend of research has been dedicated to studying the fundamentals of fixed point theorems and relaxing their assumptions with the ambition of pushing the boundaries of fixed point theory in modular spaces further. In this paper, we focus on convexity and boundedness of modulars in fixed point results taken from the literature for contractive correspondence and single-valued mappings. To relax these two assumptions, we seek to identify the ties between modular and b-metric spaces. Afterwards we present an application to a particular form of integral inclusions to support our generalized version of Nadler’s theorem in modular spaces.</p>

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

scholarly journals A new method in fixed point theory

1960 ◽  
Vol 34 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Richard G. Swan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Method
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