Picard and weakly Picard operators technique for nonlinear differential equations in Banach spaces
Journal of Mathematical Analysis and Applications, 2012 The authors study nonlocal Cauchy problems for differential equations in Banach spaces. Using Picard and weakly Picard operators technique and suitable Bielecki norms, some existence, uniqueness and data dependence results are obtained under some mild conditions. They also discuss a class of impulsive Cauchy problems by adapting the same methods.
Wang, JinRong +2 more
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Ulam-Hyers stability of fixed point equations for multivalued operators on KST spaces [PDF]
Surveys in Mathematics and its Applications, 2014 In this paper we define the notions of Ulam-Hyers stability on KST spaces and cw-weakly Picard operator for the multivalued operators case in order to establish a relation between these.
Liliana Guran Manciu
doaj
Approximation methods for hybrid diffusion systems with state-dependent switching processes : numerical algorithms and existence and uniqueness of solutions [PDF]
, 2010 By focusing on hybrid diffusions in which continuous dynamics and discrete events coexist, this work is concerned with approximation of solutions for hybrid stochastic differential equations with a state-dependent switching process.
Cao, Dingzhou +3 more
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Iterative functional-differential system with retarded argument
Journal of Numerical Analysis and Approximation Theory, 2006 Existence, uniqueness and data dependence results of solution to the Cauchy problem for iterative functional-differential system with delays are obtained using weakly Picard operator theory.
Diana Otrocol
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Krasnoselskii's theorem in generalized Banach spaces and application
Electronic Journal of Qualitative Theory of Differential Equations, 2012 The purpose of this paper is to extend Krasnoselskii's fixed point theorem to the case of generalized Banach spaces for singlevalued and multivalued operators.
I. R. Petre, Adrian Petrusel
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Linear Sigma Models With Strongly Coupled Phases -- One Parameter Models
, 2013 We systematically construct a class of two-dimensional $(2,2)$ supersymmetric gauged linear sigma models with phases in which a continuous subgroup of the gauge group is totally unbroken.
Hori, Kentaro, Knapp, Johanna
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A Volterra functional-integral equation, via weakly Picard operators technique [PDF]
Carpathian Journal of Mathematics, 2014 In this paper we consider a Volterra functional-integral equation with linear modifications of the arguments. We use weakly Picard operators’ technique and we obtain existence and data dependence results for the solutions.
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Differential equations with modified argument, via weakly Picard operators’ theory [PDF]
Carpathian Journal of Mathematics, 2013 In this paper we use Picard and weakly Picard operators technique, introduced by Ioan A. Rus, to study a class of differential equations with modified argument and a boundary value problem for this kind of equations. We obtain existence, uniqueness, comparison and data dependence results.
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Fixed points for multivalued contractions on a metric space [PDF]
Surveys in Mathematics and its Applications, 2010 The purpose of this paper is to prove a fixed point theorem for multivalued operators and a fixed point theorem for multivalued weakly Picard operators in the terms of τ -distance.
Liliana Guran
doaj
AIMS Mathematics, 2020 <abstract> <p>The aim of this paper is to introduce the notion of Suzuki type multivalued contraction with simulation functions and then to set up some new fixed point and data dependence results for these type of contraction mappings. We produce an example to support our results.
Azhar Hussain +3 more
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