Showing papers in "Annals of the West University of Timisoara: Mathematics and Computer Science in 2022"
TL;DR: In this article , the authors give sufficient conditions for Ψ − conditional exponential asymptotic stability of the Ω − bounded solutions of a nonlinear Lyapunov matrix differential equation with integral term as right side.
Abstract: Abstract The aim of this paper is to give sufficient conditions for Ψ − conditional exponential asymptotic stability of the Ψ − bounded solutions of a nonlinear Lyapunov matrix differential equation with integral term as right side.
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TL;DR: In this article , the authors considered uniform polynomial splitting for a discrete cocycle over a discrete semi-low in Banach spaces and obtained characterizations of Datko type and also in terms of Lyapunov functions.
Abstract: Abstract In this paper we consider a concept of uniform polynomial splitting for a discrete cocycle over a discrete semiflow in Banach spaces. We obtain some characterizations of Datko type and also in terms of Lyapunov functions. The study is made from the point of view of the invariant projectors and also strongly invariant projectors.
TL;DR: In this article , the authors emphasize some growth concepts for the dichotomic behavior of evolution operators in Banach spaces, such as exponential growth, polynomial growth, and h-growth.
Abstract: Abstract The aim of the present paper is to emphasize some growth concepts for the dichotomic behavior of evolution operators in Banach spaces. In fact, we approach the exponential growth, the polynomial growth and the h-growthfor both uniform and nonuniform cases. Connections between concepts are established. Majorization criteria for the uniform behaviors are given.
TL;DR: In this paper , a new approach for the fuzzy quasi-b-metric spaces is presented and some properties of these spaces are obtained, and a special attention is granted to the decomposition theorems of a fuzzy B-measure into a right continuous and ascending family of B-metrics.
Abstract: Abstract In this paper we present a new approach for the fuzzy quasi-b-metric spaces and we obtain some properties of these spaces. A special attention is granted to the decomposition theorems of a fuzzy quasi-b-metric into a right continuous and ascending family of quasi-b-metrics. Finally, some future lines of research are highlighted.
TL;DR: In this paper , the authors studied the notion of η-Einstein-like LP-Sasakian manifolds admitting Ricci solitons and showed that the potential vector field V is point-wise collinear.
Abstract: Abstract The object of the present article is to study the notion of η-Einstein-like LP-Sasakian manifolds admitting η-Ricci soliton. Furthermore, we study the η-Ricci soliton on LP-Sasakian manifolds when the potential vector field V is point-wise collinear.
TL;DR: In this article , a Cauchy problem for a fractional differential inclusion defined by a Caputo type fractional derivative is considered and a sufficient condition for local controllability along a reference trajectory in terms of a certain fractional variational differential inclusion associated to the initial problem is obtained.
Abstract: Abstract We consider a Cauchy problem for a fractional differential inclusion defined by a Caputo type fractional derivative and we obtain a sufficient condition for local controllability along a reference trajectory in terms of a certain fractional variational differential inclusion associated to the initial problem.
TL;DR: In this article , the authors presented some characterizations for the study of dichotomy of dynamical systems and derived integral characterizations of Datko type for the notion of uniform dichotomy with growth rates for skew-evolution cocycles in Banach spaces.
Abstract: Abstract The paper presents some characterizations for the study of dichotomy of dynamical systems. Integral characterizations of Datko type are considered for the notion of uniform dichotomy with growth rates, also called uniform h-dichotomy, for skew-evolution cocycles in Banach spaces.
TL;DR: In this paper , existence results for Ψ-asymptotic equivalence of two pairs of (Lyapunov) matrix differential equations with integral term as right side and modified argument are given.
Abstract: Abstract Using the notion of strict h-contraction, existence results for Ψ-asymptotic equivalence of two pairs of (Lyapunov) matrix differential equations with integral term as right side and modified argument are given.
TL;DR: In this paper , a three-dimensional mathematical model is analyzed in order to study the labour market, with an emphasis on unemployment, employment and the number of open positions, taking into account the distributed time delay.
Abstract: Abstract A three-dimensional mathematical model is analyzed in order to study the labour market, with an emphasis on unemployment, employment and the number of open positions. The rate of change of new positions created by the public and private sectors depends on the historical levels of unemployment, taking into account the distributed time delay. The non-dimensional mathematical model is done and the existence of the equilibrium points is examined. The findings related to the positivity and boundedness of solutions are presented. In addition the global asymptotic stability of the positive equilibrium is provided. The theoretical results are exemplified by the numerical simulations.
TL;DR: In this article , two notions of logarithmic dichotomy for discrete skew-evolution semi-low in Banach spaces were considered and the relation between them was established.
Abstract: Abstract The paper considers two notions of logarithmic dichotomy for discrete skew-evolution semiflows in Banach spaces. We establish the relation between them, we give a characterization for the uniform logarithmic dichotomy of Zabczyk type and a sufficient criteria for the uniform logarithmic dichotomy.
TL;DR: In this article , the authors studied the problem of fixed point structures with fixed point structure, mappings and fixed point property, and the basic results in terms of exponential with fixed-point property were given.
Abstract: Abstract In this paper we study the following problem (Problem 4.2 in, I.A. Rus, Sets with structure, mappings and fixed point property: fixed point structures, Fixed Point Theory 23, No. 2 (2022), 689-706): Let (𝒰, 𝒮, M) be a fixed point structure on (𝒰, M). We suppose that (𝒰, M) is with cartesian product. In which conditions, we have that: X,Y∈𝒮⇒X×Y∈𝒮? Some results in terms of exponential with fixed point property are also given. The basic results are illustrated by examples.
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