Application Of Fixed Point Theorem Research Articles

Applications of Fixed Point Theorems to the Problem of the Equilibrium Strategy Existence Preservation in a Parametric Family of Antagonistic Games

Applications of Fixed Point Theorems to the Problem of the Equilibrium Strategy Existence Preservation in a Parametric Family of Antagonistic Games

Derivation of Fixed-Point Theorem Using Expansive Mapping Approach

Application of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that if T:X→X is a contraction mapping on a complete metric space (X, d) then there exists a unique fixed point in X. A lot has been done on application of contraction mapping in Fixed Point Theorem on metric spaces such as Cantor set with the contraction constant of 1/3 , the Sierpinski triangle also with contraction constant of 1/2 . On the other hand, a mapping T:X → X on (X, d) such that ∀x, y ∈ X: d(Tx, Ty) ≥ d (x, y) is called an expansive mapping. There are various types of expansive mappings such as; isometry expansive mapping, proper/strict expansive mapping and anti-contraction expansive mapping. From the available literature, Fixed Point Theorem has been derived using contraction mapping approach. In this paper, we establish that it is also possible to derive Fixed Point Theorem using expansive mapping approach.

Applications of Fixed Point Theorems to Solutions of Operator Equations in Banach Spaces

In this paper we use Browder’s and Gohde’s fixed point theorem, Kirk’s fixed point theorem and the Sadovskii fixed point theorem to obtain solutions of operator equations in Banach spaces.

Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform Method

In this work, we combined two techniques, the variational iteration technique and the Laplace transform method, in order to solve some nonlinear-time fractional partial differential equations. Although the exact solutions may exist, we introduced the technique VITM that approximates the solutions that are difficult to find. Even a single iteration best approximates the exact solutions. The fractional derivatives being used are in the Caputo-Fabrizio sense. The reliability and efficiency of this newly introduced method is discussed in details from its numerical results and their graphical approximations. Moreover, possible consequences of these results as an application of fixed-point theorem are placed before the experts as an open problem.

Applications of Fixed Point Theorems to the Vacuum Einstein Constraint Equations with Non-Constant Mean Curvature

In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept of half-continuity coupled with the introduction of local supersolutions. These methods allow to: unify some recent existence results, simplify many proofs (for instance, the main theorem in arXiv:1012.2188) and weaken the assumptions of many recent results.

Applications of Fixed Point Theorems to Generalized Saddle Points of Bifunctions on Chain-Complete Posets

We apply the extensions of the Abian-Brown fixed point theorem for set-valued mappings on chain-complete posets to examine the existence of generalized and extended saddle points of bifunctions defined on posets. We also study the generalized and extended equilibrium problems and the solvability of ordered variational inequalities on posets, which are equipped with a partial order relation and have neither an algebraic structure nor a topological structure.

The applications of fixed-point theorem in optimisation problems

The applications of fixed-point theorem in optimisation problems The fixed-point theorem is widely used in different engineering applications. The present paper focuses on its applications in optimisation. A Matlab toolbox, which implements the branch-and-bound optimisation method based on the fixed-point theorem, is used for solving different real-life test problems, including estimation of model parameters for the Jiles-Atherton model.

Applications of fixed point theorems in the theory of invariant subspaces

Applications of fixed point theorems in the theory of invariant subspaces

Applications of Fixed Point Theorems in the Theory of Generalized IFS

AbstractWe introduce the notion of a generalized iterated function system (GIFS), which is a finite family of functions "Equation missing", where "Equation missing" is a metric space and "Equation missing". In case that "Equation missing" is a compact metric space and the functions "Equation missing" are contractions, using some fixed point theorems for contractions from "Equation missing" to "Equation missing", we prove the existence of the attractor of such a GIFS and its continuous dependence in the "Equation missing"'s.

Applications of Fixed Point Theorems in Divisibility of Polynomials

The aim of the present paper is to study the dynamics and fixed points of a class of functions induced by integers and then apply the fixed point theorem to obtain general tests of divisibility of numbers. In the second part, we generalize the theorems on divisibility to obtain conditions of divisibility of polynomials by (x 4 + q) type polynomials. We not only obtain generalizations of the well-known remainder theorem and the factor theorem of algebra but also compute explicit value of the quotient. The results are computationally explicit and can be easily implemented on digital computers.

A boundary value problem on an infinite interval

We are interested here in proving the existence of solutions to the (generalised) boundary value problemwhere A is a continuous n×n matrix on R+ = [0, ∞), F is a continuous n vector on R+ × S (S = a suitable subset of Rn), T is a bounded linear operator defined on (or on a subspace of) C[R+, Rn], the space of all bounded and continuous Rn-valued functions on R+, and r is a fixed vector in Rn. There is an abundance of papers dealing with the problem ((I), (II)) on finite intervals, either in its full generality (cf., for example, (1), (2), (3), (4), (6)), or for special cases of the operator T. The reader is especially referred to the work of Shreve (7), (8) for such problems on infinite intervals for scalar equations. A series representation of the solutions is given by Kravchenko and Yablonskii (5). Most of our methods are extensions of the corresponding ones on finite intervals with some variations concerning the application of fixed-point theorems. Examples of interesting operators T arewhere V(t), M, N are n×n matrices with V(t) integrable.