This paper establishes a version of Nevanlinna theory based on Jackson difference operator $D_{q}f(z)=\frac{f(qz)-f(z)}{qz-z}$ for meromorphic functions zero order in the complex plane $\mathbb{C}$. We give logarithmic lemma, second fundamental theorem, defect relation, Picard theorem and five-value sense $q$-difference operator. By using this theory, we investigate growth entire solutions line...

We give a characterization of convex functions in terms of difference among values of a function. As an application, we propose an estimation of operator monotone functions: If A > B ≥ 0 and f is operator monotone on (0,∞), then f(A)−f(B) ≥ f(‖B‖+ )−f(‖B‖) > 0, where = ‖(A−B)−1‖−1. Moreover it gives a simple proof to Furuta’s theorem: If logA > logB for A, B > 0 and f is operator monotone on (0...

Abstract. The dynamical systems method (DSM) is justified for solving operator equations F (u) = f , where F is a nonlinear operator in a Hilbert space H. It is assumed that F is a global homeomorphism of H onto H, that F ∈ C loc, that is, it has the Fréchet derivative F ′(u) continuous with respect to u, that the operator [F ′(u)]−1 exists for all u ∈ H and is bounded, ||[F ′(u)]−1|| ≤ m(u), w...

Let f be a function from R+ into itself. A classic theorem of K. Löwner says that f is operator monotone if and only if all matrices of the form [ f(pi)−f(pj) pi−pj ] are positive semidefinite. We show that f is operator convex if and only if all such matrices are conditionally negative definite and that f(t) = tg(t) for some operator convex function g if and only if these matrices are conditio...

Fabrication, Physicochemical Characterization and Evaluation of In vitro Anticancer Efficacy a Novel pH Sensitive Polymeric Nanoparticles for Efficient Delivery Hydrophobic Drug against Colon CancerManikandan Mahalingam, Kannan Krishnamoorthy

Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping, consider the induced multiplication operator Mπ : F → F given by Mπ(f)(x) := π(x)f(x), f ∈ G, x ∈ coz(F). In this paper we give necessary a...

In this article we consider four particular cases of Synthetic Aperture Radar imaging with moving objects. In each case, we analyze the forward operator F and the normal operator F ∗F , which appear in the mathematical expression for the recovered reflectivity function (i.e. the image). In general, by applying the backprojection operator F ∗ to the scattered waveform (i.e. the data), artifacts ...

Let (M,F) be a compact Riemannian foliated manifold, equipped with a bundlelike metric gM . We will also use the following notation: N ∗F is the conormal bundle to F , G is the holonomy groupoid of F . In Introduction, we will formulate our main results for the geometric case of the transverse signature operator, referring the reader to the main body of the paper for the formulations in the cas...

A unary operator f is idempotent if the equation f(x) = f(f(x)) holds. On the other end, an element a of an algebra is said to be an idempotent for a binary operator if a = a a. This paper presents a rule format for Structural Operational Semantics that guarantees that a unary operator be idempotent modulo bisimilarity. The proposed rule format relies on a companion one ensuring that certain te...

Let H be a Hilbert space of analytic functions on the unit disk D. For an analytic function ψ on D, we can define the multiplication operator Mψ : f → ψf, f ∈ H. For an analytic selfmapping φ of D, the composition operator Cφ defined on H as Cφf f ◦ φ, f ∈ H. These operators are two classes of important operators in the study of operator theory in function spaces 1–3 . Furthermore, for ψ and φ,...