scholarly journals DECOMPOSITION OF Cm THROUGH Q-PERIODIC DISCRETE EVOLUTION FAMILY

2019 ◽  
Vol 3 (1) ◽  
pp. 09-12
Author(s):  
Akbar Zada ◽  
Hafiz Ullah
Keyword(s):  
Evolution Family

scholarly journals Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with Jump

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-22
Author(s):  
Yong Xu ◽  
Ruifang Wang
Keyword(s):  
Reaction Diffusion ◽  
Evolution Family ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Averaging Principle ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Random Measures ◽  
Fast System ◽  
Stochastic Reaction

In this paper, we aim to develop the averaging principle for a slow-fast system of stochastic reaction-diffusion equations driven by Poisson random measures. The coefficients of the equation are assumed to be functions of time, and some of them are periodic or almost periodic. Therefore, the Poisson term needs to be processed, and a new averaged equation needs to be given. For this reason, the existence of time-dependent evolution family of measures associated with the fast equation is studied and proved that it is almost periodic. Next, according to the characteristics of almost periodic functions, the averaged coefficient is defined by the evolution family of measures, and the averaged equation is given. Finally, the validity of the averaging principle is verified by using the Khasminskii method.

scholarly journals Approximate Fixed Point Sequences of an Evolution Family on a Metric Space

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Si Fuan ◽  
Rizwan Ullah ◽  
Gul Rahmat ◽  
Muhammad Numan ◽  
Saad Ihsan Butt ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Nonlinear Operator ◽  
Iteration Process ◽  
Evolution Family ◽  
Nonlinear Mapping ◽  
Approximate Fixed Point ◽  
The Family ◽  
Ishikawa Iteration Process ◽  
The Common

In this article, we study the approximate fixed point sequence of an evolution family. A family E=Ux,y;x≥y≥0 of a bounded nonlinear operator acting on a metric space M,d is said to be an evolution family if Ux,x=I and Ux,yUy,z=Ux,z for all x≥y≥z≥0. We prove that the common approximate fixed point sequence is equal to the intersection of the approximate fixed point sequence of two operators from the family. Furthermore, we apply the Ishikawa iteration process to construct an approximate fixed point sequence of an evolution family of nonlinear mapping.

scholarly journals A New Estimation of the Growth Bound of a Periodic Evolution Family on Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Constantin Buse ◽  
Aftab Khan ◽  
Gul Rahmat ◽  
Afshan Tabassum
Keyword(s):  
Banach Spaces ◽  
Evolution Family ◽  
Growth Bound

Discrete Characterization of Exponential Stability of Evolution Family Over Hilbert Space

2014 ◽  
Vol 39 ◽  
pp. 281-291
Author(s):  
Nisar Ahmad ◽  
◽  
Akbar Zada ◽  
Ihsan Ullah Khan ◽  
◽  
...  
Keyword(s):  
Hilbert Space ◽  
Exponential Stability ◽  
Evolution Family

An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

2016 ◽  
Vol 94 (3) ◽  
pp. 618-631 ◽  
Author(s):  
Constantin Buşe ◽  
Donal O’Regan ◽  
Olivia Saierli
Keyword(s):  
Convolution Operator ◽  
Evolution Family ◽  
Growth Bound

scholarly journals Approximating Common Fixed Points of an Evolution Family on a Metric Space via Mann Iteration

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Liang Luo ◽  
Rizwan Ullah ◽  
Gul Rahmat ◽  
Saad Ihsan Butt ◽  
Muhammad Numan
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Irrational Number ◽  
Iteration Process ◽  
Common Fixed Points ◽  
Evolution Family ◽  
Mann Iteration ◽  
The Family ◽  
Families Of Operators ◽  
Mann Iteration Process

In this article, we present the set of all common fixed points of a subfamily of an evolution family in terms of intersection of all common fixed points of only two operators from the family; that is, for subset M of L , we have F M = F Y ϱ 1 , 0 ∩ F Y ϱ 2 , 0 , where ϱ 1 and ϱ 2 are positive and ϱ 1 / ϱ 2 is an irrational number. Furthermore, we approximate such common fixed points by using the modified Mann iteration process. In fact, we are generalizing the results from a semigroup of operators to evolution families of operators on a metric space.

scholarly journals β–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 231 ◽  
Author(s):  
Xiaoming Wang ◽  
Muhammad Arif ◽  
Akbar Zada
Keyword(s):  
Differential Equations ◽  
Type Inequality ◽  
Impulsive System ◽  
Evolution Family ◽  
Compact Interval ◽  
Ulam Stability ◽  
Basic Tool ◽  
Unbounded Interval ◽  
Nonautonomous Differential Equations ◽  
Rassias Stability

In this paper, we study a system governed by impulsive semilinear nonautonomous differential equations. We present the β –Ulam stability, β –Hyers–Ulam stability and β –Hyers–Ulam–Rassias stability for the said system on a compact interval and then extended it to an unbounded interval. We use Grönwall type inequality and evolution family as a basic tool for our results. We present an example to demonstrate the application of the main result.

scholarly journals Poxvirus protein evolution: Family wide assessment of possible horizontal gene transfer events

2009 ◽  
Vol 144 (1-2) ◽  
pp. 233-249 ◽  
Author(s):  
Mary R. Odom ◽  
R. Curtis Hendrickson ◽  
Elliot J. Lefkowitz
Keyword(s):  
Gene Transfer ◽  
Horizontal Gene Transfer ◽  
Protein Evolution ◽  
Evolution Family

scholarly journals Controllability of nonlocal non-autonomous neutral differential systems including non-instantaneous impulsive effects in 𝕉n

2020 ◽  
Vol 28 (3) ◽  
pp. 103-121
Author(s):  
Velusamy Kavitha ◽  
Mani Mallika Arjunan ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Evolution Family ◽  
Impulsive Effects ◽  
Differential Systems ◽  
First Order ◽  
Set Up

AbstractThis manuscript involves a class of first-order controllability results for nonlocal non-autonomous neutral differential systems with non-instantaneous impulses in the space 𝕉n. Sufficient conditions guaranteeing the controllability of mild solutions are set up. Concept of evolution family and Rothe’s fixed point theorem are employed to achieve the required results. A model is investigated to delineate the adequacy of the results.

On the Dichotomy of the Evolution Families: A Discrete-Argument Approach

2011 ◽  
Vol 54 (3) ◽  
pp. 527-537
Author(s):  
Ciprian Preda ◽  
Ciprian Sipos
Keyword(s):  
Banach Space ◽  
Continuous Time ◽  
Exponential Dichotomy ◽  
Evolution Family ◽  
Time Behavior ◽  
Inhomogeneous Term ◽  
Orlicz Sequence Space ◽  
Continuity Hypothesis ◽  
Vector Valued ◽  
Discrete Argument

AbstractWe establish a discrete-time criteria guaranteeing the existence of an exponential dichotomy in the continuous-time behavior of an abstract evolution family. We prove that an evolution family acting on a Banach space X is uniformly exponentially dichotomic (with respect to its continuous-time behavior) if and only if the corresponding difference equation with the inhomogeneous term from a vector-valued Orlicz sequence space lΦ(ℕ, X) admits a solution in the same lΦ(ℕ, X). The technique of proof effectively eliminates the continuity hypothesis on the evolution family (i.e., we do not assume that U( · , s)x or U(t, · )x is continuous on [s, ∞), and respectively [0, t]). Thus, some known results given by Coffman and Schaffer, Perron, and Ta Li are extended.

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