scholarly journals LINEAR VERSUS NONLINEAR ALLOCATION RULES IN RISK SHARING UNDER FINANCIAL FAIRNESS

2018 ◽  
Vol 48 (3) ◽  
pp. 995-1024 ◽  
Author(s):  
Johannes M. Schumacher
Keyword(s):  
Unique Solution ◽  
Existence And Uniqueness ◽  
Risk Sharing ◽  
Analogous Statement ◽  
Allocation Rules ◽  
Sharing Rules ◽  
Linear Rule ◽  
Pareto Efficient ◽  
The Given ◽  
Privately Owned

AbstractIn a risk exchange, participants trade a privately owned risk for a share in a pool. If participants agree on a valuation rule, it can be decided whether or not, according to the given rule, these trades take place at equal value. If equality of values holds for all participants, then the exchange is said to be “financially fair”. It has been shown by Bühlmann and Jewell (1979) that, under mild assumptions, the constraint of financial fairness singles out a unique solution among the set of all Pareto efficient risk exchanges. In this paper, we find that an analogous statement is true if we limit ourselves to linear exchanges. Conditions are provided for existence and uniqueness of linear sharing rules that are both financially fair and Pareto efficient among all linear sharing rules. The performance of the linear rule is compared to that of the general (nonlinear) rule in a number of specific cases.

On the existence and uniqueness of a nonlinear q-difference boundary value problem of fractional order

2021 ◽  
pp. 2250011
Author(s):  
Zouaoui Bekri ◽  
Vedat Suat Erturk ◽  
Pushpendra Kumar
Keyword(s):  
Difference Equation ◽  
Boundary Value Problem ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Solution Existence ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Research Collection ◽  
The Given

In this research collection, we estimate the existence of the unique solution for the boundary value problem of nonlinear fractional [Formula: see text]-difference equation having the given form [Formula: see text] [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] represents the Caputo-type nonclassical [Formula: see text]-derivative of order [Formula: see text]. We use well-known principal of Banach contraction, and Leray–Schauder nonlinear alternative to vindicate the unique solution existence of the given problem. Regarding the applications, some examples are solved to justify our outcomes.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

3D Object Modeling Using Sketches

2013 ◽  
pp. 238-256
Author(s):  
Sofia Kyratzi ◽  
Nickolas S. Sapidis
Keyword(s):  
Unique Solution ◽  
User Interaction ◽  
Solid Model ◽  
Object Modeling ◽  
Step Process ◽  
3D Object ◽  
Partial View ◽  
The Given ◽  
3D Object Modeling

In this paper, the authors present a new algorithm for constructing a solid model when the given input is only one partial-view sketch (“natural sketch”). This algorithm is a two-step process, where first a complete (wireframe) sketch is derived, which is then transformed into a 3D polyhedron. The paper details topological and geometric aspects of the process, as well as the essential “user-interaction” components dealing with cases where the sketch-to-solid problem does not have a unique solution.

scholarly journals A Hybrid Contraction that Involves Jaggi Type

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 715
Author(s):  
Erdal Karapınar ◽  
Andreea Fulga
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Hybrid Type ◽  
Fractional Differential ◽  
The Given ◽  
Type Contraction

In this manuscript, we aim to provide a new hybrid type contraction that is a combination of a Jaggi type contraction and interpolative type contraction in the framework of complete metric spaces. We investigate the existence and uniqueness of such a hybrid contraction in separate theorems. We consider a solution to certain fractional differential equations as an application of the given results. In addition, we provide an example to indicate the genuineness of the given results.

scholarly journals Iterative Solution for Systems of a Class of Abstract Operator Equations in Banach Spaces and Application

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Hua Su
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Iterative Solution ◽  
Order Method ◽  
Operator Equations ◽  
Abstract Operator ◽  
Uniqueness Of A Solution

In this paper, by using the partial order method, the existence and uniqueness of a solution for systems of a class of abstract operator equations in Banach spaces are discussed. The result obtained in this paper improves and unifies many recent results. Two applications to the system of nonlinear differential equations and the systems of nonlinear differential equations in Banach spaces are given, and the unique solution and interactive sequences which converge the unique solution and the error estimation are obtained.

scholarly journals Admissible Hybrid Z-Contractions in b-Metric Spaces

Axioms ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 2 ◽  
Author(s):  
Ioan Cristian Chifu ◽  
Erdal Karapınar
Keyword(s):  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Uniqueness Result ◽  
Point Problem ◽  
Well Posedness ◽  
Simulation Functions ◽  
Set Up ◽  
The Given

In this manuscript, we introduce a new notion, admissible hybrid Z -contraction that unifies several nonlinear and linear contractions in the set-up of a b-metric space. In our main theorem, we discuss the existence and uniqueness result of such mappings in the context of complete b-metric space. The given result not only unifies the several existing results in the literature, but also extends and improves them. We express some consequences of our main theorem by using variant examples of simulation functions. As applications, the well-posedness and the Ulam–Hyers stability of the fixed point problem are also studied.

Functions of Minimal Norm with the Given Set of Fourier Coefficients

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 651
Author(s):  
Pyotr Ivanshin
Keyword(s):  
Fourier Series ◽  
Existence And Uniqueness ◽  
Fourier Coefficients ◽  
Nonnegative Function ◽  
Trigonometric Fourier Series ◽  
Minimum Norm ◽  
Minimal Norm ◽  
Uniqueness Of The Solution ◽  
The Given

We prove the existence and uniqueness of the solution of the problem of the minimum norm function ∥ · ∥ ∞ with a given set of initial coefficients of the trigonometric Fourier series c j , j = 0 , 1 , … , 2 n . Then, we prove the existence and uniqueness of the solution of the nonnegative function problem with a given set of coefficients of the trigonometric Fourier series c j , j = 1 , … , 2 n for the norm ∥ · ∥ 1 .

scholarly journals On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Areej S. S. Alharbi ◽  
Hamed H. Alsulami ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Admissible Function ◽  
Point Theory ◽  
Contractive Condition ◽  
Simulation Function ◽  
The Given ◽  
Admissible Functions

We investigate the existence and uniqueness of certain operators which form a new contractive condition via the combining of the notions of admissible function and simulation function contained in the context of completeb-metric spaces. The given results not only unify but also generalize a number of existing results on the topic in the corresponding literature.

scholarly journals Plane Waves Scattered by a Spherical Inclusion in a Half Space of Poroelastic Material

2020 ◽  
Vol 03 (02) ◽  
pp. 1-1
Author(s):  
Doo-Sung Lee ◽  
Keyword(s):  
Half Space ◽  
Existence And Uniqueness ◽  
Spherical Inclusion ◽  
Plane Waves ◽  
Spherical Wave ◽  
Wave Functions ◽  
Successive Approximations ◽  
Compressional Waves ◽  
Poroelastic Material ◽  
The Given

This paper concerns a poroelastic half-space in which plane compressional waves are scattered by a spherical inclusion. Addition theorems for the spherical wave functions are utilized to meet the boundary conditions on the plane, and the satisfaction of the given conditions on the boundary of the sphere leads to three infinite series equations, whose solution can be acquired by successive approximations. Further, its existence and uniqueness are discussed.

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