Fixed Point Theorem

We prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a lower solution. To this aim, we prove an appropriate fixed point theorem in partially ordered sets.

The aim of this paper is to establish the existence of at least one solution for a general inequality of quasi-hemivariational type, whose solution is sought in a subset K of a real Banach space E. First, we prove the existence of solutions in the case of compact convex subsets and the case of bounded closed and convex subsets. Finally,

In this paper, we deal with a class of semilinear elliptic equation in a bounded domain $\Omega\subset\mathbb{R}^N$, $N\geq 3$, with $C\sp{1,1}$ boundary. Using a new fixed point result of the Krasnoselskii's type for the sum of two operators, an existence principle of strong solutions is proved. We give two examples where the nonlinearity can be critical.

*Apresentação feita na Jornada de Pós Graduação 2019 da UFSM* O presente trabalho tem como objetivo apresentar de modo simples as bases conceituais e técnicas lógico-matemáticas utilizadas por Kurt Gödel em seu artigo Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I para demonstrar que, em um sistema formal T que comporte o mínimo de Aritmética em seu conjunto de sentenças básicas é incompleto, ou seja, há sentenças enunciadas formalmente em T que são verdadeiras, porém indemonstráveis neste sistema (Primeiro Teorema de Gödel), e que não há como demonstrar a consistência do sistema formal por ele mesmo (Segundo Teorema). Focando na prova do primeiro teorema, faremos uma introdução aos termos gerais dos quais exige-se um entendimento prévio. Em seguida abordaremos um breve contexto histórico, os tipos de paradoxos e quais são relacionados a estratégia e estrutura de prova de Gödel (assim como de outras provas de incompletude), bem como sua técnica de aritmetização de sentenças, o método de prova por diagonalização e o recurso da autorreferência em sentenças de T e a exposição do Teorema do Ponto Fixo, apresentando ao final o esboço da prova do primeiro teorema da incompletude como um caso particular de tal teorema em T.

Guided by a passage in Kreisel, this is a discussion of the relations between the phenomena in the title, with special attention to the method of analysis and synthesis in Greek geometry, fixed point theorems, and Kreisel's contact with Gödel.

The aim of this paper is to present some fixed point theorems for generalized contractions by altering distance functions in a complete cone metric spaces endowed with a partial order. We also general-ize fixed point theorems of J. Harjani, K. Sadarangani [J. Harjani, K. ...

The paper aims at reconstructing the historical sequence of mathematical
works through which the fixed-point technique entered the tool-box of modern
economics and at establishing a link between this sequence and the neoclassical
approach to economic modeling. The focus is on the change in the demonstration
techniques caused by the spread of the so-called formalist approach to mathematical
economics. This change was embodied by the fixed-point technique.
The main conclusions of the paper are that the formalist revolution marked a
dramatic discontinuity in the history of economic theory and that early game
theory – despite having been the gateway through which the fixed-point entered
economics – was only partly responsible for such a discontinuity.

The epsilon calculus contains terms of the form 'εxFx' for every predicate in the language.  This means that it includes what I shall call 'empty' terms (when there are no Fs) and also what I shall call 'indexical' terms (when there is more then one F).  These particular terms give the epsilon calculus a very distinctive character in comparison with the standard predicate calculus.  For instance, an 'empty' term is central to understanding how we can do things that Russell and Whitehead's Principia Mathematica cannot do, in connection with Gödel's Theorems.  And attention to 'indexical' terms is crucial to solving the major Logical Paradoxes that have been a puzzle for over a century.  Most particularly they are crucial to the solution of what has been called 'Gödel's Paradox', which has been claimed to show that natural language is
paraconsistent.

In recent years, the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, with few examples of applications in bioengineering are high lighted in the literature. The methods of fractional calculus, when defined as a Laplace, Sumudu or Fourier convolution product, are suitable for solving many problems in emerging biomedical research. The electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. Application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law stress-strain relationship for modeling biomaterials. Fractional operations by following the original approach...

We deal with semilinear functional special random impulsive differential equations in this paper. Contraction mapping principle is used to study the existence and uniqueness of the mild solution of the system. Again we have established ulam stabilities, exponential stability and stability of the system, where the sufficient conditions for stability is established using continuous dependence on initial conditions. Also an example is included to verify the concepts and basic results in this paper.