About Me
Welcome to my personal website! I am Dagnachew Jenber, A university lecturer at Addis Ababa Science and Technology University. Currently, I am a PhD student at Bahir Dar University. My research interests include Functional Analysis, Fractional Calculus, and Number Theory. I am passionate about teaching, research, and solving real-world mathematical problems.
Selected Papers
Current Project
The study of mathematical mappings and their associated problems has been a cornerstone of mathematical analysis and optimization. Over the years, various classes of problems have been introduced to address specific needs in applied mathematics, engineering, and computer science. Among these, the split common fixed point problem, split null point problem, split equality fixed point problem, split variational inequality problem, split equilibrium problem, and split variational inclusion problem have garnered significant attention due to their wide range of applications in fields such as signal processing, image reconstruction, and network theory.
The split common fixed point problem, for instance, involves finding a point that is simultaneously a fixed point of two or more mappings, each defined on different spaces. This problem is crucial in scenarios where solutions need to satisfy multiple criteria across different domains. Similarly, the split null point problem and split equality fixed point problem extend these ideas to include conditions of nullity and equality, respectively, further broadening the scope of potential applications.
The split variational inequality problem and split equilibrium problem introduce additional layers of complexity by incorporating inequality constraints and equilibrium conditions, respectively. These problems are particularly relevant in economic modeling and game theory, where equilibrium states and optimal strategies are of interest. The split variational inclusion problem, on the other hand, generalizes these concepts by considering inclusions rather than equations, allowing for a more flexible frame work that can accommodate a wider variety of constraints and conditions.
Despite the extensive research on these problems, there remains a need for more general classes of mappings and problems that can unify and extend these existing frame- works. This project aims to introduce such a class of mappings and problems, providing a more comprehensive and versatile approach to addressing complex mathematical challenges. By constructing algorithms that converge to the solutions of these newly introduced problems within the framework of real Banach spaces, this project not only advances theoretical understanding but also offers practical tools for solving real-world problems.
The choice of real Banach spaces as the underlying framework is motivated by their rich structure and generality, which allow for the accommodation of a wide range of functional spaces encountered in applications. The development of convergent algorithms in this setting is a significant contribution, as it ensures that the theoretical advancements can be effectively translated into computational solutions. In summary, this Project seeks to expand the boundaries of current mathematical problem solving paradigms by introducing new classes of mappings and problems, and by developing robust algorithms for their resolution. This project promises to enhance both the theoretical landscape and practical toolkit available to researchers and practitioners in various fields.