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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
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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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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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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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, 2020 In this paper, by employing fixed-point methods, we obtain the existence and uniqueness results for the nonlinear implicit fractional differential equations in Banach spaces. Further, we obtain the uniqueness, dependence of the solution on the initial condition as well as on the functions involved on the right-hand side by means of Picard and weakly ...
Sutar, Sagar T., Kucche, Kishor D.
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On some properties of the Picard operators [PDF]
, 1990 summary:We consider the Picard operators $\mathcal{P}_n$ and $\mathcal{P}_{n;r}$ in exponential weighted spaces.
Rempulska, Lucyna +5 more
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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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From a Dieudonne theorem concerning the Cauchy problem to an open problem in the theory of weakly Picard operators [PDF]
Carpathian Journal of Mathematics, 2014 Let (X, d) be a complete metric space and let f : X → X be a self operator. In this paper we study the following two problems: Problem 1. Let f be such that its fixed points set is a singleton, i.e., Ff = {x∗}. Under which conditions the next implication does hold: f is asymptotically regular ⇒ f is a Picard operator? Problem 2.
Berinde, Vasile +2 more
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Qualitative properties of functional differential equation
Electronic Journal of Qualitative Theory of Differential Equations, 2014 The aim of this paper is to discuss some basic problems (existence and uniqueness, data dependence) of the fixed point theory for a functional differential equation with an abstract Volterra operator. In the end an application is given.
Diana Otrocol, Veronica Ilea
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Advanced Science, EarlyView.Pathological tissue rigidity mechanoprimes microglia by enhancing actin cytoskeleton–nucleus coupling and chromatin opening at rigidity‐responsive cis‐regulatory elements (mechanoCREs). Subsequent NF‐κB/p65 signaling converges on this permissive regulatory state to amplify inflammatory gene expression and microglial activation.
Yu Xuan Meng +15 more
wiley +1 more source