This paper deals with new methods for approximating a solution to the fixed point problem; find x̃ ∈ F T , where H is a Hilbert space, C is a closed convex subset of H, f is a ρ-contraction from C into H, 0 < ρ < 1, A is a strongly positive linear-bounded operator with coefficient γ > 0, 0 < γ < γ/ρ, T is a nonexpansive mapping on C, and PF T denotes the metric projection on the set of fixed poi...

in this paper, a complete description concerning linear operators of banach spaces with range in lipschitz algebras $lip_al(x)$ is provided. necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. finally, a lower bound for the essential norm of such operators is obtained.

Lyapunov equation. We analyze the approximation properties of solutions of abstract Lyapunov equations in the setting of a scale of Hilbert spaces associated to an unbounded diagonalizable operator which satisfies the Kato’s square root theorem. We call an (unbounded) operator A diagonalizable if there exists a bounded operator Q, with a bounded inverse, such that the (unbounded) operator Q−1AQ...

In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to ...

Let X denote a complete separable metric space, and let C(X) denote the linear space of all bounded continuous real-valued functions on X. The Lie generator of a strongly continuous semigroup T of continuous transformations in X is the linear operator in C(X) consisting of all ordered pairs (f; g) such that f; g 2 C(X), and for each x 2 X, g(x) is the derivative at 0 of f(T()x). We completely c...

We constructed a summation–integral type operator based on the latest research in linear positive operators area. establish some approximation properties for this new operator. highlight qualitative part of presented operator; we studied uniform convergence, Voronovskaja-type theorem, and Grüss–Voronovskaja result. Our subsequent study focuses direct theorem using Ditzian–Totik modulus smoothne...

In this paper, we study frames for bounded linear operators and defined the notion of Ad-operator frame for Banach spaces. A necessary and sufficient condition for a sequence of bounded linear operators to be an Ad-operator frame has been given. Some characterizations of Ad-operator frames have been discussed. Further, a method has been given to generate a -Banach frame using a Schauder frame. ...

1.1 (Fredholm operators). Let X, Y be real Banach spaces and denote their dual spaces by X, Y . A bounded linear operator D : X → Y is called Fredholm if it has a closed image and if its kernel and cokernel (the quotient space Y/imD) are finite dimensional. Equivalently, there exists a bounded linear operator T : Y → X such that the operators TD− idX and DT − idY are compact. The Fredholm index...