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An intersection theorem for set-valued mappings

Ravi P. Agarwal, Mircea Balaj, Donal O'Regan (2013)

Applications of Mathematics

Given a nonempty convex set X in a locally convex Hausdorff topological vector space, a nonempty set Y and two set-valued mappings T : X ⇉ X , S : Y ⇉ X we prove that under suitable conditions one can find an x ∈ X which is simultaneously a fixed point for T and a common point for the family of values of S . Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.

An iterative algorithm by viscosity approximation method for mixed equilibrium problems, variational inclusion and fixed point of an infinite family of pseudo-contractive mappings

Phayap Katchang, Poom Kumam (2011)

Banach Center Publications

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusion problems for inverse strongly monotone mappings and the set of common fixed points for an infinite family of strictly pseudo-contractive mappings in the setting of Hilbert spaces. We prove the strong convergence theorem by using the viscosity approximation method for finding the common element of the above four...

An Ulam stability result on quasi-b-metric-like spaces

Hamed H. Alsulami, Selma Gülyaz, Erdal Karapınar, İnci M. Erhan (2016)

Open Mathematics

In this paper a class of general type α-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.

Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

Vuk Milišić, Alfio Quarteroni (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that guarantee...

Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

Vuk Milišić, Alfio Quarteroni (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that...

Another fixed point theorem for nonexpansive potential operators

Biagio Ricceri (2012)

Studia Mathematica

We prove the following result: Let X be a real Hilbert space and let J: X → ℝ be a C¹ functional with a nonexpansive derivative. Then, for each r > 0, the following alternative holds: either J’ has a fixed point with norm less than r, or s u p | | x | | = r J ( x ) = s u p | | u | | L ² ( [ 0 , 1 ] , X ) = r ∫ 0 1 J ( u ( t ) ) d t .

Applications of contractive-like mapping principles to fuzzy equations

Juan J. Nieto, Rosana Rodríguez López (2006)

Revista Matemática Complutense

We recall a recent extension of the classical Banach fixed point theorem to partially ordered sets and justify its applicability to the study of the existence and uniqueness of solution for fuzzy and fuzzy differential equations. To this purpose, we analyze the validity of some properties relative to sequences of fuzzy sets and fuzzy functions.

Applications of the spectral radius to some integral equations

Mirosława Zima (1995)

Commentationes Mathematicae Universitatis Carolinae

In the paper [13] we proved a fixed point theorem for an operator 𝒜 , which satisfies a generalized Lipschitz condition with respect to a linear bounded operator A , that is: m ( 𝒜 x - 𝒜 y ) ≺ A m ( x - y ) . The purpose of this paper is to show that the results obtained in [13], [14] can be extended to a nonlinear operator A .

Currently displaying 201 – 220 of 258