Papers by Buthainah A. Ahmed
Weighted shift operators and extended eigenvalues
Journal of Interdisciplinary Mathematics
Let H be a Hilbert space. A complex number is named the extended eigenvalue for an operator T ∈ B... more Let H be a Hilbert space. A complex number is named the extended eigenvalue for an operator T ∈ B(H), if there is operator not equal zero X ∈ B(H) so that: TX = mXT and X are named as extended eigen operator for an operator T opposite to m. The goal of this work is to find extended eigenvalues and extended eigen operators for shift operators J, Ja, K, Ka such that J : I2 (ℕ) → I2 (ℕ) and K : I2 (ℕ) → I2 (ℕ) defined by: Jen = e2n , and Ken = { (en/2 if n even) (0 if n odd), for all x ∈ l2(ℕ). Furthermore, the closeness of extended eigenvalues for all of these shift operators under multiplication has been proven.
Ibn AL-Haitham Journal For Pure and Applied Sciences
The study of fixed points on the maps fulfilling certain contraction requirements has several ap... more The study of fixed points on the maps fulfilling certain contraction requirements has several applications and has been the focus of numerous research endeavors. On the other hand, as an extension of the idea of the best approximation, the best proximity point (ƁƤƤ) emerges. The best approximation theorem ensures the existence of an approximate solution; the best proximity point theorem is considered for addressing the problem in order to arrive at an optimum approximate solution. This paper introduces a new kind of proximal contraction mapping and establishes the best proximity point theorem for such mapping in fuzzy normed space ( space). In the beginning, the concept of the best proximity point was introduced. The concept of proximal contractive mapping in the context of fuzzy normed space is then presented. Following that, the best proximity point theory for this kind of mapping is established. In addition, we provide an example application of the results
Complex C1C2 symmetric and finite rank operators
Journal of Interdisciplinary Mathematics
An operator A in B(H) is called complex C1C2-symmetric if E two antilinear, isometric and involut... more An operator A in B(H) is called complex C1C2-symmetric if E two antilinear, isometric and involution C1, C2 such that C1A = A* C2 (A=C1A*C2). In this paper, we shows that when the rank one operator become C1C2-symmetirc operators. Moreover, we show that the compact operator is C1C2 -symmetric operator. Also, we award some examples of C1C2-symmetric operators.
Iraqi Journal of Science
In this paper, we generalize the definition of fuzzy inner product space that is introduced b... more In this paper, we generalize the definition of fuzzy inner product space that is introduced by Lorena Popa and Lavinia Sida on a complex linear space. Certain properties of the generalized fuzzy inner product function are shown. Furthermore, we prove that this fuzzy inner product produces a Nadaban-Dzitac fuzzy norm. Finally, the concept of orthogonality is given and some of its properties are proven.
Iteration for a Non-Self -Strongly Pseudocontractive Map
Iraqi journal of science, 2013
Extended Eigenvalues and Eigenoperators of Some Weighted Shift Operators
Iraqi journal of science, Feb 28, 2023
Baghdad Science Journal
The best proximity point is a generalization of a fixed point that is beneficial when the contrac... more The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced. After that, the best proximity point theorem for such type of mapping in a fuzzy normed space is state and prove. In addition, the idea of α ̃–ϕ ̃-proximal contractive mapping is presented in a fuzzy normed space and under specific conditions, the bes...
Indonesian Journal of Electrical Engineering and Computer Science
The best proximity point is a generalization of a fixed point that is beneficial when the contrac... more The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems provide an approximate solution to the fixed-point equation Tҳ = ҳ. It is used to solve the problem to determine an approximate solution that is optimum. The main goal of this paper is to present new types of proximal contraction for nonself mappings in a fuzzy Banach space. At first, the notion of the best proximity point is presented. We introduce the notion of α ̌–η ̌-β ̌ proximal contractive. After that, the best proximity point theorem for such type of mappings in a fuzzy Banach space is proved. In addition, the concept of α ̌–η ̌-φ ̌ proximal contractive mapping is presented in a fuzzy Banach space and under specific conditions, the best proximity point theorem for such type of mapping is proved. Additionally, some examples are supplied to show the results' applicability.
Iraqi Journal of Science
In this paper, we present a concept of nC- symmetric operator as follows: Let A be a bounded lin... more In this paper, we present a concept of nC- symmetric operator as follows: Let A be a bounded linear operator on separable complex Hilbert space , the operator A is said to be nC-symmetric if there exists a positive number n (n such that CAn = A*ⁿ C (An = C A*ⁿ C). We provide an example and study the basic properties of this class of operators. Finally, we attempt to describe the relation between nC-symmetric operator and some other operators such as Fredholm and self-adjoint operators.
Ibn AL-Haitham Journal For Pure and Applied Sciences
In this paper, developed Jungck contractive mappings into fuzzy Jungck contractive and p... more In this paper, developed Jungck contractive mappings into fuzzy Jungck contractive and proved fuzzy fixed point for some types of generalize fuzzy Jungck contractive mappings.
C1 C2- symmetric operators for some types of operators
Journal of Physics: Conference Series
In this paper, we give some new properties of C1C2-symmetric operators and discuss some results a... more In this paper, we give some new properties of C1C2-symmetric operators and discuss some results about these kind of operators. Also, we describe the conditions that a binormal operator becomes normal operator and give necessary and sufficient conditions that C1C2- symmetric operators becomes a binormal operator. Finally, we solve the problem that a binormal operator is not closed under addition.
Generalized Weyl's Theorem for Elementary Operators with Some Classes of Operators
Al-Mustansiriyah Journal of Sciences, 2013
Stability of Royalty (𝒂𝒎) under Perturbations
On C1C2 symmetric operators
Journal of Interdisciplinary Mathematics, Oct 28, 2021
Abstract Let C 1 and C 2 are conjugation operators (both are antiliner, isometric and invoulation... more Abstract Let C 1 and C 2 are conjugation operators (both are antiliner, isometric and invoulation) on a separable complex Hilbert space H. In this paper, we present the notion of C 1 C 2- symmetric operators as: A bounded linear operator A on H is C 1 C 2-symmetric operators if C 1 A = A* C 2 (A = C 1 A*C 2). We study and discuss several properties and give an example for such kind of operators.
Description of Completeness for a partial metric space and fixed points
The equivalence between fixed point property and the completeness of a partial metric space was s... more The equivalence between fixed point property and the completeness of a partial metric space was studied under some conditions for single valued and set valued mappings. Also Kennan type mapping using to characterize the completeness of partial metric spaces.
Iraqi Journal for Computer Science and Mathematics, 2022
The aim of this paper is to study new results of an approximate orthogonality of Birkhoff-James t... more The aim of this paper is to study new results of an approximate orthogonality of Birkhoff-James techniques in real Banach space , namely Chiemelinski orthogonality (even there is no ambiguity between the concepts symbolized by orthogonality) and provide some new geometric characterizations which is considered as the basis of our main definitions. Also, we explore relation between two different types of orthogonalities. First of them orthogonality in a real Banach space and the other orthogonality in the space of bounded linear operator . We obtain a complete characterizations of these two orthogonalities in some types of Banach spaces such as strictly convex space, smooth space and reflexive space. The study is designed to give different results about the concept symmetry of Chmielinski-orthogonality for a compact linear operator on a reflexive, strictly convex Banach space having Kadets-Klee property by exploring a new type of a generalized some results with Birkhoff James orthogon...
Iraqi Journal of Science, 2022
In this paper, we introduce new concepts that relates to soft space based on work that w... more In this paper, we introduce new concepts that relates to soft space based on work that was previously presented by researchers in this regard. First we give the definition of Soft Contraction Operator and some examples. After that we introduce the concepts of soft Picard iteration and soft Mann iteration processes. We also give some examples to illustrate them. Many concepts in normed spaces have been generalized in soft normed spaces. One of the important concepts is the concept of stability of soft iteration in soft normed spaces. We discuss this concept by giving some lemmas that are used to prove some theorems about stability of soft iteration processes (with soft contraction operator) with soft Picard iteration procedure as well as soft Mann iteration procedure.
Iraqi Journal of Science, 2019
In this paper we investigate the stability and asymptotic stability of the zero solution for... more In this paper we investigate the stability and asymptotic stability of the zero solution for the first order delay differential equation where the delay is variable and by using Banach fixed point theorem. We give new conditions to ensure the stability and asymptotic stability of the zero solution of this equation.
In this paper we study the property of the operator equations 2 = S SRS and 2 = R RSR where S is ... more In this paper we study the property of the operator equations 2 = S SRS and 2 = R RSR where S is a *-paranormal operator we show that if S or * S is a polynomial root of *-paranormal operator then gW A f ) ( for all )) ( ( A H f , where } , , { R RS SR A and we show that For the operator equation 2 = S SRS and 2 = R RSR we have ) ( = ) ( = ) ( = ) ( R RS SR S
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Papers by Buthainah A. Ahmed