This paper present results of $\omega$-order preserving partial contraction mapping generating a regular weak*-continuous semigroup. We consider a semigroup on a Banach space $X$ and $B:X^\odot\rightarrow X^*$ is bounded, then the intertwining formula was used to define a semigroup $T^B(t)$ on $X^*$ which extends the perturbed semigroup $T^B_0(t)$ on $X^\odot$ using the variation of constants formula. We also investigated a certain class of weak*-continuous semigroups on dual space $X^*$ which contains both adjoint semigroups and their perturbations by operators $B:X^\odot\rightarrow X^*$.
In this paper, we present results of $\omega$-order preserving partial contraction mapping creating a continuous time Markov semigroup. We use Markov and irreducible operators and their integer powers to describe the evolution of a random system whose state changes at integer times, or whose state is only inspected at integer times. We concluded that a linear operator $P:\ell^{1}(X_+)\rightarrow \ell^{1}(X_+)$ is a Markov operator if its matrix satisfies $P_{x,y}\geqslant 0$ and $\sum_{x\in X_+}P_{x,y=1}$ for all $y\in X$.
This paper is concerned with modification of the Adomian Decomposition Method for solving linear and non-linear Volterra and Volterra-Fredholm Integro-Differential equations. The Modified form of ADM was carried out by replacing the Adomian polynomials constructed in the conventional Adomian Decomposition Method with the constructed canonical polynomials. The modified Adomian Decomposition Method was applied to solve some existing example. The results obtained using the newly modified ADM proved superior when compared with the conventional ADM.
In this paper, spectral mapping theorem for the point spectrum on infinitesimal generator of a C0-semigroup was further investigated. Toeplitz properties of semigroup considering ω-order preserving partial contraction mapping (ω − OCPn) as a semigroup of linear operator was established to obtained new results. We also consider A ∈ ω − OCPn which is the infinitesimal generator of a C0-semigroup using the Spectral Mapping Theorem (SMT) to obtain the relationships between the spectrum of A and the spectrum of each of the operators {T (t), t ≥ 0}.
This paper consists of the results about \(\omega\)-order preserving partial contraction mapping using perturbation theory to generate a one-parameter semigroup. We show that adding a bounded linear operator \(B\) to an infinitesimal generator \(A\) of a semigroup of the linear operator does not destroy A's property. Furthermore, \(A\) is the generator of a one-parameter semigroup, and \(B\) is a small perturbation so that \(A+B\) is also the generator of a one-parameter semigroup.
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