In what follows, the symbol X stands for a real Banach space with norm ‖ · ‖ and (normalized) duality mapping J. Moreover, “continuous” means “strongly continuous” and the symbol “→” (“⇀”) means strong (weak) convergence. The symbol R (R+) stands for the set (−∞,∞) ([0,∞)) and the symbols ∂D, intD, D denote the strong boundary, interior and closure of the set D, respectively. An operator T : X ...

A class of scalar Stieltjes like functions is realized as linear-fractional transformations of transfer functions of conservative systems based on a Schrödinger operator Th in L2[a,+∞) with a non-selfadjoint boundary condition. In particular it is shown that any Stieltjes function of this class can be realized in the unique way so that the main operator A of a system is an accretive (∗)-extensi...

It is well known that a densely defined operator A on a Hilbert space is accretive if and only if A has a contractive H∞-calculus for any angle bigger than π 2 . A third equivalent condition is that ‖(A− w)(A + w)−1‖ ≤ 1 for all Rew ≥ 0. In the Banach space setting, accretivity does not imply the boundedness of the H∞-calculus any more. However, we show in this note that the last condition is s...

We present here a correction to an error in our paper [3]. We are grateful to Dachun Yang for bringing the error to our attention. In [3] we develop a theory of H1 (Hardy type) and BMO spaces adapted to a second order, divergence form elliptic (aka accretive) operator L in Rn, with complex, L∞ coefficents. In particular we establish the equivalence of several different H1 type spaces, based on ...

‎the purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex banach space which has a‎ ‎uniformly g^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function ...

vi List of Figures xiii List of Equations xvi List of Tables xvi Chapter 1 Accretive and compositional change in natural and artificial evolution 1 1.1 Exchange between evolutionary biology and evolutionary computation 2 1.1.1 Gradualism and the probability of large adaptive changes 2 1.1.2 Evolutionary adaptation and artificial optimisation methods 3 1.2 Accretive and compositional mechanisms ...

The main contributions of this paper is twofold. First, our primary concern to suggest a new iterative algorithm using the P-?-proximal-point mapping technique and Nadler?s for finding approximate solutions system generalized multi-valued nonlinear variational-like inclusions. Under some appropriate conditions imposed on parameters mappings involved in inclusions, strong convergence sequences g...