Browsing by Author "Altiparmak, Ebru"

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Approximation Properties of a New Type of Gamma Operator by Two Parameter Gamma Function
(Univ Nis, Fac Sci Math, 2024) Altiparmak, Ebru; Demir, Seda; Icoz, Gurhan
In this work, with the aid of the two parameter Gamma function, we define a new type of the Gamma operator. We have proved Voronovskaya type theorem and rate of convergence. We establish uniform convergence of a sequence of the new type Gamma operator via power series method. The power series method is also used to analyze the rate of convergence of operators. Finally, numerical examples are given to show the approximate properties of the new type Gamma operator.
Fixed Point Results in Partially Ordered Partial BV(s)-Metric Spaces
(Semnan University, 2021) Altiparmak, Ebru; Karahan, Ibrahim
In this paper, some fixed point results for generalized Geraghty type alpha-admissible contractive mappings and rational type generalized Geraghty contraction mappings are given in partially ordered partial b(v) (s)-metric spaces. Also, a modified version of a partial b(v) (s)-metric space is defined and a fixed point theorem is proved in this space. Finally, some examples are given related to the results.
Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial Bv(s)-Metric Spaces
(Univ Maragheh, 2021) Altiparmak, Ebru; Karahan, Ibrahim
In this paper, necessary and sufficient conditions for the existence and uniqueness of fixed points of generalized Geraghty type contraction mappings are given in complete partial b(v)(s)-metric spaces. The results are more general than several results that exist in the literature because of the considered space. A numerical example is given to support the obtained results. Also, the existence and uniqueness of the solutions of an integral equation has been verified considered as an application.
A Modified Inertial Viscosity Algorithm for an Infinite Family of Nonexpansive Mappings and Its Application to Image Restoration
(Amer. Inst. Mathematical Sciences-AIMS, 2024) Altiparmak, Ebru; Karahan, Ibrahim
. The image restoration problem is one of the popular topics in image processing studied by many authors because of its applications in various areas. This paper aims to present a new algorithm using viscosity approximation with inertial effect to find a common fixed point of an infinite family of nonexpansive mappings in a Hilbert space and obtain more quality images from degenerate images. Some strong convergence theorems are proved under mild conditions. The obtained results are applied to solve monotone inclusion problems, convex minimization problems, variational inequality problems, and generalized equilibrium problems. It is shown that the proposed algorithm performs better than some other algorithms. Also, the effects of inertial and viscosity terms in the algorithm on image restoration are investigated.
A Modified Preconditioning Algorithm for Solving Monotone Inclusion Problem and Application to Image Restoration Problem
(University Politehnica Bucharest, Sci Bull, 2022) Altiparmak, Ebru; Karahan, Ibrahim
In this work, we propose a modified preconditioning inertial viscosity forward-backward algorithm. We also study strong convergence behaviour of our algorithm under mild assumptions in a real Hilbert space. We use the proposed algorithm to solve the convex minimization problem. Finally, we apply our algorithm for solving the image restoration problems. We can say that the proposed algorithm exhibit to outperform the already existing algorithms in the literature.
A New Preconditioning Algorithm for Finding a Zero of the Sum of Two Monotone Operators and Its Application to Image Restoration Problems
(Taylor & Francis Ltd, 2022) Altiparmak, Ebru; Karahan, Ibrahim
Finding a zero of the sum of two monotone operators is one of the most important problems in monotone operator theory, and the forward-backward algorithm is the most prominent approach for solving this type of problem. The aim of this paper is to present a new preconditioning forward-backward algorithm to obtain the zero of the sum of two operators in which one is maximal monoton and the other one is M-cocoercive, where M is a linear bounded operator. Furthermore, the strong convergence of the proposed algorithm, which is a broader variant of previously known algorithms, has been proven in Hilbert spaces. We also use our algorithm to tackle the convex minimization problem and show that it outperforms existing algorithms. Finally, we discuss several image restoration applications.
Pre-Conditioning CQ Algorithm for Solving the Split Feasibility Problem and Its Application to Image Restoration Problem
(Taylor & Francis Ltd, 2025) Altiparmak, Ebru; Jolaoso, Lateef Olakunle; Karahan, Ibrahim; Rehman, Habib ur
In this study, we define two pre-conditioning CQ algorithms for the split feasibility problem by using self-adaptive and line-search techniques in the real Hilbert space. One of the self-adaptive techniques is used to obtain optimal step size. These techniques do not require prior knowledge of the operator norm or estimation of the matrix norm. We also establish weak convergence theorems with respect to particular norms. As an application, numerical experiments show that the proposed algorithm is effective in image restoration problem.