The fixed point theory of multi-valued mappings in topological vector spaces

1968 ◽  
Vol 177 (4) ◽  
pp. 283-301 ◽  
Author(s):  
Felix E. Browder
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Vector Spaces ◽  
Topological Vector Spaces

scholarly journals w-b-Cone Distance and Its Related Results: A Survey

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 171 ◽  
Author(s):  
Reza Babaei ◽  
Hamidreza Rahimi ◽  
Manuel De la Sen ◽  
Ghasem Soleimani Rad
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Vector Spaces ◽  
Minkowski Functionals ◽  
Topological Vector Spaces

In this work, we define the concept of a w-b-cone distance in t v s -cone b-metric spaces which differs from generalized c-distance in cone b-metric spaces, and we discuss its properties. Our results are significant, since all of the results in fixed point theory with respect to a generalized c-distance can be introduced in the version of w-b-cone distance. Moreover, using Minkowski functionals in topological vector spaces, we prove the equivalence between some fixed point results with respect to a w t -distance in general b-metric spaces and a w-b-cone distance in t v s -cone b-metric spaces.

scholarly journals Erratum: Abdou, A. A. N. and Khamsi, M.A. Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces ℓp(·). Mathematics 2020, 8, 76

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 578
Author(s):  
Afrah A. N. Abdou ◽  
Mohamed Amine Khamsi
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Variable Exponent ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Sequence Spaces ◽  
Vector Spaces ◽  
Nonexpansive Maps ◽  
Banach Contraction

Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces lp(·). We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before.

scholarly journals Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces ℓp(·)

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 76 ◽  
Author(s):  
Afrah Abdou ◽  
Mohamed Khamsi
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Variable Exponent ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Sequence Spaces ◽  
Vector Spaces ◽  
Nonexpansive Maps ◽  
Banach Contraction

Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces ℓ p ( · ) . We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before.

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.

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