Department of Mathematics
URI for this collectionhttps://rps.wku.edu.et/handle/123456789/45781
Department of Mathematics
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Item BEST PROXIMITY POINT THEOREMS FOR GENERALIZED WEAKLY CONTRATIVE MAPPING IN METRIC SPACES(WOLKITE UNIVERSITY, 2020-12) AWOL MOHAMMEDThe 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.Item LargeNon-Local Operator and Applications(WOLKITE UNIVERSITY, 2021-06) Abera Dijago; Dr. Hailu BikilaIn 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.Item 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.Item 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.Item NUMERICAL SOLUTION OF LINEAR FREEHOLD INTEGRAL EQUATION OF BY USING NEWTON-COTES QUADRATURE METHOD(Wolkite University, 2023-06-20) SHEGA GASHAWIn this thesis, we discussed the numerical solution of the linear Fredholm integral equation by using the Newton-cotes quadrature rule and the Lagrange interpolation method. Lin ear Fredholm integral equation which can not be easily evaluated analytically. This thesis was concerned with the numerical method. Newton-cotes quadrature method was used to transform the linear Fredholm integral equation into a system algebraic equation. It shows that the approximate solution is uniformly convergent to the exact solution. In addition to demonstrating the efficiency and applicability of the proposed method, several numerical examples are included which confirm the convergent results. After introducing the type of integral equation we were investigate some numerical methods for solving the Freehold in tegral equation of the second kind. For the numerical treatment of the Freehold integral equation, we implemented the following numerical method; the Quadrature method and the Trapezoidal rule. The mathematical framework of these numerical method with their convergence properties was presented. These numerical method will be illustrated by some numerical examples. Comparisons between these method was drawn.Item THE BEST PROXIMITY POINT THEOREM FOR GENERALIZED (χ,φ)- WEAK CONTRACTIONS IN BRANCIARI TYPE GENERALIZED METRIC SPACES(WOLKITE UNIVERSITY, 2025-06) SHEMSU WABELA HULCHAFOThe Theorem of "Best Proximity Point for generalized (χ,φ)-weak contractions in Branciari type generalized metric spaces" is thoroughly examined in this thesis. The concept of contraction mappings is generalized by the (χ,φ)-weak contraction. By defining the situations in which a mapping has a "unique best proximity point", this thesis applies the Theorem of "Best Proximity Point" to this context. Examples are provided to illustrate the results and show how the theorem might be applied in different situationsItem BEST PROXIMITY THEOREM FOR GENERALIZED (θ,γ)-PROXIMAL CONTRACTION MAPPING IN RECTANGULAR QUASI B- METRIC SPACE(WOLKITE UNIVERSITY, 2025-06-10) KASAHUN BEYENE BEJIGAThis paper explores best proximity point theorems whit in the framework of broad (θ,γ) proximal reduction “mappings in rectangular quasi b-metric spaces”. “We introduce the class of rectangular quasi b- metric” space as a broadening of rectangular metric space, “rectangular quasi” b-metric space, “rectangular b-metric” space,define broad (θ,γ)proximal reduction mappings. Establish situation under which a optimal proximity point exists and provide example to clear my results. Extend previous work on fixed point theorems and contribute to the theory of proximity points in non-standard metric spaces.