Search results for "action principle"
showing 7 items of 7 documents
Fixed point theorems for fuzzy mappings and applications to ordinary fuzzy differential equations
2014
Abstract Ran and Reurings (Proc. Am. Math. Soc. 132(5):1435-1443, 2004) proved an analog of the Banach contraction principle in metric spaces endowed with a partial order and discussed some applications to matrix equations. The main novelty in the paper of Ran and Reurings involved combining the ideas in the contraction principle with those in the monotone iterative technique. Motivated by this, we present some common fixed point results for a pair of fuzzy mappings satisfying an almost generalized contractive condition in partially ordered complete metric spaces. Also we give some examples and an application to illustrate our results. MSC:46S40, 47H10, 34A70, 54E50.
Self-modeling epistemic spaces and the contraction principle
2020
What Graziano and colleagues describe as the “attention schema” really is one special case of what I have called the “phenomenal model of the intentionality relation” (PMIR) since 1993 (Metzinger, ...
Energy and Personality: A Bridge between Physics and Psychology
2021
[EN] The objective of this paper is to present a mathematical formalism that states a bridge between physics and psychology, concretely between analytical dynamics and personality theory, in order to open new insights in this theory. In this formalism, energy plays a central role. First, the short-term personality dynamics can be measured by the General Factor of Personality (GFP) response to an arbitrary stimulus. This GFP dynamical response is modeled by a stimulus¿response model: an integro-differential equation. The bridge between physics and psychology appears when the stimulus¿response model can be formulated as a linear second order differential equation and, subsequently, reformulat…
Fixed point theorems for -contractive type mappings
2012
Abstract In this paper, we introduce a new concept of α – ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.
Best Proximity Points for Some Classes of Proximal Contractions
2013
Given a self-mapping g: A → A and a non-self-mapping T: A → B, the aim of this work is to provide sufficient conditions for the existence of a unique point x ∈ A, called g-best proximity point, which satisfies d g x, T x = d A, B. In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function x → d g x, T x, thereby getting an optimal approximate solution to the equation T x = g x. An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-s…
Fixed points of α-type F-contractive mappings with an application to nonlinear fractional differential equation
2016
Abstract In this paper, we introduce new concepts of α-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from α-GF-contractions given in [8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an application to nonlinear fractional differential equation are given to illustrate the usability of the new theory.
Systematic derivation of partial differential equations for second order boundary value problems
2022
Software systems designed to solve second order boundary value problems are typically restricted to hardwired lists of partial differential equations. In order to come up with more flexible systems, we introduce a systematic approach to find partial differential equations that result in eligible boundary value problems. This enables one to construct and combine one's own partial differential equations instead of choosing those from a pre-given list. This expands significantly end users possibilities to employ boundary value problems in modeling. To introduce the main ideas we employ differential geometry to examine the mathematical structure involved in second order boundary value problems …