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jih-3023
Convergence To Approximate Solutions of Multivalued Operators
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The goal of this study is to provide a new explicit iterative process method  approach for solving maximal monotone(M.M )operators in Hilbert spaces utilizing a finite family of different types of  mappings as( nonexpansive mappings,resolvent mappings and projection mappings. The findings given in this research strengthen and extend key previous findings in the literature. Then, utilizing various structural conditions in Hilbert space and variational inequality problems, we examine the strong convergence to nearest point projection for these explicit iterative process methods Under the presence of two important conditions for convergence, namely closure and convexity. The findings reported in this research strengthen and extend key previous findings from the literature

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Publication Date
Sun Oct 27 2019
Journal Name
Iraqi Journal Of Science
The convergence of Iteration Scheme to Fixed Points in Modular Spaces
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     The aim of this paper is to study the convergence of an iteration scheme for multi-valued mappings which defined on a subset of a complete convex real modular. There are two main results, in the first result, we show that the convergence with respect to a multi-valued contraction mapping to a fixed point. And, in the second result, we deal with two different schemes for two multivalued  mappings (one of them is a contraction and other has a fixed point) and then we show that the limit point of these two schemes is the same. Moreover, this limit will be the common fixed point the two mappings.

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Publication Date
Sun Jan 30 2022
Journal Name
Iraqi Journal Of Science
Convergence of Iterative Algorithms in Cat(0) Spaces
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     In this article, results have been shown via using a general quasi contraction multi-valued mapping in Cat(0) space. These results are used to prove the convergence of two iteration algorithms to a fixed point and the equivalence of convergence. We also demonstrate an appropriate conditions to ensure that one is faster than others.

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Publication Date
Sun Sep 05 2010
Journal Name
Baghdad Science Journal
Quasi-posinormal operators
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In this paper, we introduce a class of operators on a Hilbert space namely quasi-posinormal operators that contain properly the classes of normal operator, hyponormal operators, M–hyponormal operators, dominant operators and posinormal operators . We study some basic properties of these operators .Also we are looking at the relationship between invertibility operator and quasi-posinormal operator .

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Publication Date
Sun Jul 30 2023
Journal Name
Iraqi Journal Of Science
The Class of Weakly Normal Operators
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     Our purpose in this paper is to introduce new operators on Hilbert space which is called weakly normal operators. Some basic properties of these operators are studied in this research. In general, weakly normal operators need not be normal operator, -normal operators and quasi-normal operators.

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Publication Date
Sat Apr 30 2022
Journal Name
Iraqi Journal Of Science
Convergence Theorems of Three-Step Iteration Algorithm in CAT (0) Spaces
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      In this paper, a modified three-step iteration algorithm for approximating a joint fixed point of non-expansive and contraction mapping is studied. Under appropriate conditions, several strong convergence theorems and Δ-convergence theorems are established in a complete CAT (0) space. a numerical example is introduced to show that this modified iteration algorithm is faster than other iteration algorithms. Finally, we prove that the modified iteration algorithm is stable. Therefore these results are extended and improved to a novel results that are stated by other researchers. Our results are also complement to many well-known theorems in the literature. This type of research can be played a vital role in computer programming

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Publication Date
Sun Jul 31 2022
Journal Name
Iraqi Journal Of Science
nC-symmetric operators
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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* C (An = C A* 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.

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Publication Date
Mon Apr 24 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Statistical Approximation Operators
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   In this paper we obtain some statistical approximation results for a general class of maxproduct operators including the paused linear positive operators.

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Publication Date
Sat Sep 30 2023
Journal Name
Iraqi Journal Of Science
Efficient Approximate Analytical Methods to Solve Some Partial Differential Equations
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     The goal of this research is to solve several one-dimensional partial differential equations in linear and nonlinear forms using a powerful approximate analytical approach. Many of these equations are difficult to find the exact solutions due to their governing equations. Therefore, examining and analyzing efficient approximate analytical approaches to treat these problems are required. In this work, the homotopy analysis method (HAM) is proposed. We use convergence control parameters to optimize the approximate solution. This method relay on choosing with complete freedom an auxiliary function linear operator and initial guess to generate the series solution. Moreover, the method gives a convenient way to guarantee the converge

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Publication Date
Fri Apr 01 2022
Journal Name
Baghdad Science Journal
On Hereditarily Codiskcyclic Operators
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Many codiskcyclic operators on infinite-dimensional separable Hilbert space do not satisfy the criterion of codiskcyclic operators. In this paper, a kind of codiskcyclic operators satisfying the criterion has been characterized, the equivalence between them has been discussed and the class of codiskcyclic operators satisfying their direct summand is codiskcyclic. Finally, this kind of operators is used to prove that every codiskcyclic operator satisfies the criterion if the general kernel is dense in the space.

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Publication Date
Sun Jan 30 2022
Journal Name
Iraqi Journal Of Science
Convergence and Stability of Iterative Scheme for a Monotone Total Asymptotically Non-expansive Mapping
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    In this work, we introduce Fibonacci– Halpern iterative scheme ( FH scheme) in partial ordered Banach space (POB space) for monotone total asymptotically non-expansive mapping (, MTAN mapping) that defined on weakly compact convex subset.  We also  discuss the results of weak and strong convergence for this scheme.

 Throughout  this work, compactness condition of m-th iterate  of the mapping for some natural m is necessary to ensure strong convergence, while Opial's condition has been employed to show weak convergence. Stability of FH scheme is also  studied. A numerical comparison is provided by an example to show that FH scheme is faster than Mann and Halpern iterative

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