Browsing by Author "Solomon Bekele"

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    Early Post-Operative Morbidities Following Early Versus Delayed Sigmoidectomy After Sigmoid Volvulus
    (Addis Ababa University, 2024-12-02) Habtamu Atalel; Solomon Bekele
    Sigmoid volvulus (SV) is characterized by the abnormal twisting of the sigmoid colon on its mesentery. It is the number one cause of acute LBO in Ethiopia. The incidence of SV varies among different regions. In Western countries, it accounts for 1-5% of all colonic obstructions, while in Ethiopia, it accounts for 58-69% of the LBO. It has a high recurrence rate of about 30 % to 80% and a significant mortality rate reaching 25–50% in some case series. According to the current practice guidelines, patients who present with uncomplicated SV are initially managed by endoscopic decompression followed by Sigmoidectomy. Sigmoidectomy carries inherent risks, including surgical site infections, anastomotic leaks, and cardio-respiratory complications. The study aimed to assess the early postoperative outcome of index and elective Sigmoidectomies.
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    Solution Methods of Monotone Inclusion Problems, Equilibrium Problems and Fixed Point Problems in Banach Spaces
    (Addis Ababa University, 2024-09) Solomon Bekele; Mengistu Goa; Habtu Zegeye; Sebsibe Teferi
    In this dissertation, we discuss four fixed point approximation methods that can be applied to solve optimization problems, differential equations, variational inequalities and equilibrium problems. In the first main result of the dissertation, we propose an inertial algorithm for solving split equality of monotone inclusion and fixed point of Bregman relatively f-nonexpansive mapping problems in reflexive real Banach spaces and established strong convergence theorems for the algorithm. Secondly, we establish a strong convergence theorem for approximating a common element of sets of solutions of a finite family of generalized mixed equilibrium problem, sets of semi-fixed points of a finite family of continuous semi-pseudocontractive mappings and sets of solutions of a finite family of variational inequality for a finite family of monotone and L-Lipschitz mappings in Banach spaces. Thirdly, we constructed and proved a strong convergence of an algorithm for approximating a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of f-fixed points of a finite family of f-pseudocontractive mappings and the set of solutions of a finite family of variational inequality problems for Lipschitz monotone mappings in real reflexive Banach spaces. In the fourth main result of the dissertation, we introduce an iterative process which converges strongly to a common point of sets of solutions of a finite family of generalized equilibrium problems, fixed points of a finite family of continuous asymptotically quasi-ϕ-nonexpansive mapping in intermediate sense, and zeros of a finite family of γ-inverse strongly monotone operators in uniformly convex and uniformly smooth real Banach space. We give numerical examples to demonstrate the behavior of the convergence of the algorithms analysed in each of the four main results of the thesis.
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    Solution Methods of Monotone Inclusion Problems, Equilibrium Problems and Fixed Point Problems in Banach Spaces
    (Addis Ababa University, 2024-09) Solomon Bekele; Mengistu Goa; Habtu Zegeye; Sebsibe Teferi
    In this dissertation, we discuss four fixed point approximation methods that can be applied to solve optimization problems, differential equations, variational inequalities and equilibrium problems. In the first main result of the dissertation, we propose an inertial algorithm for solving split equality of monotone inclusion and fixed point of Bregman relatively f-nonexpansive mapping problems in reflexive real Banach spaces and established strong convergence theorems for the algorithm. Secondly, we establish a strong convergence theorem for approximating a common element of sets of solutions of a finite family of generalized mixed equilibrium problem, sets of semi-fixed points of a finite family of continuous semi-pseudocontractive mappings and sets of solutions of a finite family of variational inequality for a finite family of monotone and L-Lipschitz mappings in Banach spaces. Thirdly, we constructed and proved a strong convergence of an algorithm for approximating a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of f-fixed points of a finite family of f-pseudocontractive mappings and the set of solutions of a finite family of variational inequality problems for Lipschitz monotone mappings in real reflexive Banach spaces. In the fourth main result of the dissertation, we introduce an iterative process which converges strongly to a common point of sets of solutions of a finite family of generalized equilibrium problems, fixed points of a finite family of continuous asymptotically quasi-ϕ-nonexpansive mapping in intermediate sense, and zeros of a finite family of γ-inverse strongly monotone operators in uniformly convex and uniformly smooth real Banach space. We give numerical examples to demonstrate the behavior of the convergence of the algorithms analysed in each of the four main results of the thesis.