Data Dependence, Strict Fixed Point Results, and Well-Posedness of Multivalued Weakly Picard Operators [PDF]
Journal of Mathematics, 2021 In this paper, we introduce the notion of s , r -contractive multivalued weakly Picard ...
Azhar Hussain +3 more
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Implicit functional differential equations with linear modification of the argument, via weakly Picard operator theory [PDF]
Carpathian Journal of Mathematics, 2021 "Let \mathbf{K}:=\mathbf{R}\text{ or }\mathbf{C},\text{ \ }0<\lambda <1 and f \in C([0,b] \times \textbf{K}^3,\textbf{K}). In this paper we use the weakly Picard operator theory technique to study the following functional-differential equation $$ y'(x)=f(x,y(x),y'(x),y(\lambda x)), x \in [0,b].$$ "
ANTON S. MUREŞAN, VIORICA MUREŞAN
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Ulam-Hyers stability for partial differential inclusions
Electronic Journal of Qualitative Theory of Differential Equations, 2012 Using the weakly Picard operator technique, we will present Ulam-Hyers stability results for integral inclusions of Fredholm and Volterra type and for the Darboux problem associated to a partial differential inclusion.
V. Lazar
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Multivalued Pseudo-Picard Operators and Fixed Point Results
Journal of Function Spaces and Applications, 2013 We introduce the concept of multivalued pseudo-Picard (MPP) operator on a metric space. This concept is weaker than multivalued weakly Picard (MWP) operator, which is given by M. Berinde and V. Berinde (2007).
Gülhan Mınak, Özlem Acar, Ishak Altun
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Dynamics and Ulam Stability for Fractional q-Difference Inclusions via Picard Operators Theory
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In this manuscript, by using weakly Picard operators we investigate the Ulam type stability of fractional q-difference An illustrative example is given in the last section.
Abbas Saïd +2 more
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Systems of functional-differential equations with maxima, of mixed type
Electronic Journal of Qualitative Theory of Differential Equations, 2014 In this paper we study some properties of the solutions of a second order system of functional-differential equations with maxima, of mixed type, with ``boundary" conditions. We use Perov's fixed point theorem and the weakly Picard operator technique.
Diana Otrocol
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Heuristic introduction to weakly Picard operator theory [PDF]
Creative Mathematics and Informatics, 2014 In this paper we study the impact of weakly Picard operator theory, [see I. A. Rus, Picard operators and applications, Sc. Math. Japonicae, 58 (2003), No. 1, 191–219] on the following problem: what can we do in order to find conditions under which a given operator is a weakly Picard operator?
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Iterated function systems consisting of continuous functions satisfying Banach’s orbital condition
Annals of the West University of Timisoara: Mathematics and Computer Science, 2018 We introduce the concept of iterated function system consisting of continuous functions satisfying Banach’s orbital condition and prove that the fractal operator associated to such a system is weakly Picard. Some examples are provided.
Miculescu Radu +2 more
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A class of abstract Volterra equations, via weakly Picard operators technique [PDF]
Mathematical Inequalities & Applications, 2010 Summary: We consider the following abstract Volterra equations: \[ x(t) = G(t,g(x)(t),x(t),x(0)) + \int ^t_{-t} K (t,s,x(s),x(h(s)))\,ds,\quad t \in \mathbb R \] and \[ x(t) = G(t,g(x)(t),x(t),x(0)) + \int ^{|t|}_{-|t|} K (t,s,x(s),x(h(s)))\,ds,\quad t \in\mathbb R.
Şerban, M. A. +2 more
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The Theory of Reich's Fixed Point Theorem for Multivalued Operators
Fixed Point Theory and Applications, 2010 The purpose of this paper is to present a theory of Reich's fixed point theorem for multivalued operators in terms of fixed points, strict fixed points, multivalued weakly Picard operators, multivalued Picard operators, data dependence of the fixed ...
Tania Lazăr +3 more
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