Department of Mathematics

URI for this collectionhttps://rps.wku.edu.et/handle/123456789/45781

Department of Mathematics

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    LargeNon-Local Operator and Applications
    (WOLKITE UNIVERSITY, 2021-06) Abera Dijago; Dr. Hailu Bikila
    In this project we discuss on,the Laplace and Fourier transform that we have found, so useful for solving the integral transforms to a general class of a non-local operators that share a common set of properties. The so called lin earities define a class of Laplace and Fourier transform which include many of the previous transform as special cases.The linearity of both transform helps to identify those assumptions that are needed to define Laplace and Fourier transform with the properties that we require a certain techniques to solve the function by using non-local operators.
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    BEST PROXIMITY POINT THEOREMS FOR GENERALIZED WEAKLY CONTRATIVE MAPPING IN METRIC SPACES
    (WOLKITE UNIVERSITY, 2020-12) AWOL MOHAMMED
    The purpose of this study is to introduce the notion of generalized proximal weakly contractive mappings in metric spaces and to prove existence and uniqueness of best proximity point for generalized proximal weakly contractive mappings in complete metric spaces. I given example to analyze and support my results.
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    BEST PROXIMITY POINT RESULTS FOR SUZUKI TYPE GENERALIZED(Ψ − Φ)-WEAK PROXIMAL CONTRACTION MAPPINGS IN METRIC SPACE
    (WOLKITE UNIVERSITY, 2021-08) AWOL MOHAMMED,
    In this project, I introduce a new Suzuki type generalized (ψ − φ)-weak proximal con traction mappings in metric space and prove the existence of the best proximity point for such mappings in a complete metric space. I provide examples to illustrate the result.My result extends some of the results in the literature.
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    ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES
    (WOLKITE UNIVERSITY, 2021-08) Teka Gidreta; Hailu Bikila (PhD)
    This project work is mainly concerned with the question of the existence and unique ness solution of the IVP in linear first order ODE’s in Banach space.That is dy dx = f(x, y), y(x0) = y0,where f is Lipschitz continuous function.So that to show the exis tence and uniqueness solution of IVP of ODE’s we will use Picard’s Theorem and iter ation method.Firstly, state and prove Banach-Cacciopoli theorem that has been applied to prove the Picard’s Existence and Uniqueness Theorem.This theorem also provides a constructive procedures(called iteration) by which to get a better approximation to the solution of ODE.