New Class Of Operators Research Articles

On some generalized recent operators in topological Spaces

In this paper we introduce a new classes of operators namely (regular generalized*, regular generalized**, generalized **regular) (briefly, rg*, rg **, g**r, respectively) in topological spaces and study some of their properties with some important theorems.

D-hyponormal and D-quasi-hyponormal Operators

New classes of operators named D-hyponormal, and D-quasi-hyponormal are introduced in this paper. Some basic properties of these operators are presented. An investigation of extensions of the Fuglede-Putnam theorem for D-hyponormal operators is given.

GENERALIZED PARTIAL MEET AND KERNEL CONTRACTIONS

AbstractTwo of the most well-known belief contraction operators are partial meet contractions (PMCs) and kernel contractions (KCs). In this paper we propose two new classes of contraction operators, namely the class of generalized partial meet contractions (GPMC) and the class of generalized kernel contractions (GKC), which strictly contain the classes of PMCs and of KCs, respectively. We identify some extra conditions that can be added to the definitions of GPMCs and of GKCs, which give rise to some interesting subclasses of those classes of functions, namely the classes of extensional and of uniform GPMCs/GKCs. In the context of contractions on belief sets the classes of partial meet contractions, uniform GPMCs and extensional GPMCs are all identical. Nevertheless, when considered as operations on belief bases, the class of uniform GPMCs coincides with the class of partial meet contractions, but the extensional GPMCs constitute a new kind of belief base contraction functions whose characterizing postulate of irrelevance of syntax is extensionality—the same postulate of irrelevance of syntax which occurs in the classical axiomatic characterization of partial meet contractions for belief sets—rather than the postulate of uniformity—which is the irrelevance of syntax postulate used in the axiomatic characterization for partial meet contractions on belief bases. Analogous results are obtained regarding the classes of extensional and of uniform GKCs. We present the interrelations in the sense of inclusion among all the new classes of operators presented in this paper and several well known classes of PMCs and of KCs.

The class of poly. normal operators

In this paper, we introduce a new class of operators on separable Hilbert space called poly. normal operator. An operator is called poly. normal if there exists a polynomial ℙ, where such that , where * is the adjoint operator of . We investigated some basic properties and new results were discussed in this research.

Structural and Spectral Properties of k-Quasi Class Q(N) and k-Quasi Class Q*(N) Operators

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce two new classes of operators: k−quasi class Q(N ) and k−quasi class Q*(N ). An operator T ∈ L(H) is of k−quasi class Q(N ) for a fixed real number N ≥ 1 and k a natural number, if T satisfies N ∥T^k+1(x)∥^2 ≤ ∥T^k+2(x)∥^2 + ∥T^k(x)∥^2, for all x ∈ H. An operator T ∈ L(H) is of k−quasi class Q*(N ) for a fixed real number N ≥ 1 and k a natural number, if T satisfiesN ∥T*T^k(x)∥^2 ≤ ∥T^k+2(x)∥^2 + ∥T^k(x)∥^2, for all x ∈ H. We study structural and spectral properties of these classes of operators. Also we compare this new classes of operators with other known classes of operators

Applying fixed point methodologies to solve a class of matrix difference equations for a new class of operators

The goal of this paper is to present a new class of operators satisfying the Prešić-type rational η-contraction condition in the setting of usual metric spaces. New fixed point results are also obtained for these operators. Our results generalize, extend, and unify many papers in this direction. Moreover, two examples are derived to support and document our theoretical results. Finally, to strengthen our paper and its contribution to applications, some convergence results for a class of matrix difference equations are investigated.

(f*-Ҩ) QUASI BINORMAL OPERATOR OF ORDER ղ

In this paper, we introduce a new class of operators on Hilbert space called (f*-Ҩ) quasi binormal operator of order ղ. We study this operator and give some of its properties.

On M−quasi Paranormal Operators

In this paper we introduce a new class of operators called M−quasi paranormal operators. A bounded linear operator T in a complex Hilbert space H is said to be a M−quasi paranormal operator if it satisfies ∥T 2x∥ 2 ≤ M∥T 3x∥ · ∥T x∥, ∀x ∈ H, where M is a real positive number. We prove basic properties, the structural and spectral properties of this class of operators.

Generalized blending type Bernstein operators based on the shape parameter λ

In the present paper, we construct a new class of operators based on new type Bézier bases with a shape parameter λ and positive parameter s. Our operators include some well-known operators, such as classical Bernstein, α-Bernstein, generalized blending type α-Bernstein and λ-Bernstein operators as special case. In this paper, we prove some approximation theorems for these operators. Approximation properties of our operators are illustrated on graphs for variables s, α, λ, and n. It should be mentioned that our operators for lambda =1 have better approximation than Bernstein and α-Bernstein operators.

Multidimensional directional derivatives and AM-FM dual-band image demodulation by higher order Teager-Kaiser operators

In this work we tackle the problem of demodulation of multidimensional AM-FM signals by multidirectional higher order Teager-Kaiser operators. This new class of operators extends those reported in the literature, which are restricted to partial derivatives. We illustrate this class of operators on signals made up of two components (bi-band signals). We show that this mixture of bi-band multidimensional AM-FM signals extends a solution of the fourth-order generating differential equation (GDE). This result generalizes the findings reported in [1] to multidimensional case. Coefficients of GDE expressed in terms of Teager-Kaiser energy operators of higher orders, yield estimates for the instantaneous amplitude and frequency of each component of the multidimensional signal in any direction. To resolve the sign ambiguity problem of the estimated frequency components of the frequency vector, a relative signs estimation strategy is presented. Three frequency estimation algorithms are developed. To show the effectiveness of the introduced new class of operators and the interest of directional derivatives, demodulation results on synthetic and real images are presented and analyzed. We compare our results to methods of the literature. Capability of the methods to track signal demodulation is measured by the norm of demodulation error and also by the well known structural similarity index measure. Even the aim of this paper is focused on bi-band multidimensional AM-FM signals, we report promising preliminary results on tri-band signals showing that the present work can be extended to more than two components.

Q-Power Quasi Binormal Operator

In this paper we introduce a new class of operators on Hilbert space called q-power quasi binormal operator. We study this operator and give some properties of it.

W-Power N-Binormal Operator on Hilbert Space

In this paper we present a new class of operators on Hilbert space called w-power n-binormal operator. We study this operator and give some properties of it.

Approximate fixed points of operators on modular G-metric spaces

In this paper, we will first introduce the approximate fixed point property and a new class of operators and contraction mapping for a cyclic map T on modular G-metric spaces. Also, we prove two general lemmas regarding approximate fixed Point of cyclic maps on modular G-metric spaces. Using these results we prove several approximate fixed point theorems for a new class of operators and contraction mapping on modular G-metric spaces.

Structure of k‐Quasi‐(m, n)‐Isosymmetric Operators

The investigation of new operators belonging to some specific classes has been quite fashionable since the beginning of the century, and sometimes it is indeed relevant. In this study, we introduce and study a new class of operators called k‐quasi‐(m, n)‐isosymmetric operators on Hilbert spaces. This new class of operators emerges as a generalization of the (m, n)‐isosymmetric operators. We give a characterization for any operator to be k‐quasi‐(m, n)‐isosymmetric operator. Using this characterization, we prove that any power of an k‐quasi‐(m, n)‐isosymmetric operator is also an k‐quasi‐(m, n)‐isosymmetric operator. Furthermore, we study the perturbation of an k‐quasi‐(m, n)‐isosymmetric operator with a nilpotent operator. The product and tensor products of two k‐quasi‐(m, n)‐isosymmetries are investigated.

Extension of m‐Symmetric Hilbert Space Operators

We introduce a new class of operators, which we will call the class of P‐quasi‐m‐symmetric operators that includes m‐symmetric operators and k‐quasi m‐symmetric operators. Some basic structural properties of this class of operators are established based on the operator matrix representation associated with such operators.

Inequalities Involving A‐Numerical Radius and Operator A‐Norm for a Class of Operators Related to (α, β) − A‐Normal Operators

In this article, we introduce and study a new class of operators, larger than (α, β) − A‐normal operators and different than (α, β) − A‐normal operators, named m‐quasi‐(α, β) − A‐normal operators. Considering the semi‐inner product induced by a positive operator A, the m‐quasi‐(α, β) − A‐normal operators turn into a generalization (for this new structure) of classical m‐quasi‐(α, β)‐normal operators. Several results concerning properties of this kind of operators are presented in the paper. Several inequalities for the A‐numerical radius and A‐operator norm for members of this class are established.

Orthogonally Biadditive Operators

In this article, we introduce and study a new class of operators defined on a Cartesian product of ideal spaces of measurable functions. We use the general approach of the theory of vector lattices. We say that an operator T : E × F ⟶ W defined on a Cartesian product of vector lattices E and F and taking values in a vector lattice W is orthogonally biadditive if all partial operators T y : E ⟶ W and T x : F ⟶ W are orthogonally additive. In the first part of the article, we prove that, under some mild conditions, a vector space of all regular orthogonally biadditive operators O B A r E , F ; W is a Dedekind complete vector lattice. We show that the set of all horizontally-to-order continuous regular orthogonally biadditive operators is a projection band in O B A r E , F ; W . In the last section of the paper, we investigate orthogonally biadditive operators on a Cartesian product of ideal spaces of measurable functions. We show that an integral Uryson operator which depends on two functional variables is orthogonally biadditive and obtain a criterion of the regularity of an orthogonally biadditive Uryson operator.

On Bilinear Narrow Operators

In this article, we introduce a new class of operators on the Cartesian product of vector lattices. We say that a bilinear operator T:E×F→W defined on the Cartesian product of vector lattices E and F and taking values in a vector lattice W is narrow if the partial operators Tx and Ty are narrow for all x∈E,y∈F. We prove that, for order-continuous Köthe–Banach spaces E and F and a Banach space X, the classes of narrow and weakly function narrow bilinear operators from E×F to X are coincident. Then, we prove that every order-to-norm continuous C-compact bilinear regular operator T is narrow. Finally, we show that a regular bilinear operator T from the Cartesian product E×F of vector lattices E and F with the principal projection property to an order continuous Banach lattice G is narrow if and only if |T| is.

Almost BS-Compact Operators and Domination Problem

Let X and Y be two Banach spaces. A bounded operator $$T: X \longrightarrow Y$$ is said to be a BS-compact operator whenever T sends Banach-Saks subsets of X onto norm compact sets of Y. In this paper, our central focus is upon introducing the class of almost BS-compact operators. The paper rests essentially on two parts. The first is devoted to the connection of this new class of operators with classical notions of operators, such as BS-compact operators, AM-compact operators, and Dunfort-Pettis operators. The second part is dedicated to the domination problem within the framework of (almost) BS-compact operators.

Equivalence of Certain Iteration Processes Obtained by Two New Classes of Operators

The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.