Department of Mathematics
URI for this collectionhttps://rps.wku.edu.et/handle/123456789/45781
Department of Mathematics
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Item COMMON BEST PROXIMITY POINT RESULTS FOR MULTI-VALUED CYCLIC MAPPINGS ON PARTIAL METRIC SPACES(wolkite University, 2025-02-28) AZIZEW ABATEThis thesis investigates best proximity point theory as a natural generalization of classical fixed point results to non-self mappings. The study focuses on generalized (α,T)-contraction mappings, cyclic and multi-valued in partial metric spaces. By unifying concepts from Hausdorff metric space and partial metric spaces, we develop existence and uniqueness theorems for best proximity points under various contractive conditions. The results extend the principle to provide new insights into cyclic and multi-valued mappings. Illustrative examples are presented to verify the applicability of the findingsItem OPTICAL PROPERTIES OF SMALL SPHERICAL PURE METAL IN PASSIVE AND ACTIVE HOST MATRICES(Wolkite University, 2021-12-17) Girma Berga KeretaIn this thesis, we have studied the optical properties of small spherical pure metal in active and passive host matrix. One of the optical properties we have investigated by this work is the local eld enhancement factor for small spherical pure metal in passive and active host matrix. The results show that for small spherical pure metal there is only one maxima of the local eld enhancement factor in both the passive and active host matrix. We present an analytical and numerical method for optical bistability of small spherical pure metal in passive and active host matrix. Using the derived analytical and numerical results we calculated the cubic equation of the optical bistability of small spherical pure metal embedded in passive and active host matrix. To observe considerable di erences on the onset and o set parts of the plots of optical bistability for the active host matrix, we took the integer multiples for the imaginary part of dielectric function of the host matrix ( ′′ h), (i.e. ′′ h = −2, ′′ h = −3 and ′′ h = −4). The third main target of study was to derive the analytical and numerical results of the real and imaginary parts of refractive indices for small spherical pure metal embedded in a host matrix. We have plotted the graphs of the real and imaginary parts of the refractive indices of the analytical and numerical results for small spherical pure metal in active and passive host matrix. The numerical and analytical results show that the local eld enhancement factor is extremely enhanced, the optical bistability activation and the real and imaginary parts of the refactive index are increased when the small spherical pure metal is embedded in active host matrix (i.e. the natural or original property of the imaginary part of the dilectric function of the host matrix is a ected by applying additionalexternal dilectric function on the host matrix).Item THE BEST PROXIMITY POINT THEOREM FOR GENERALIZED (χ, φ) - WEAK CONTRACTIONS IN BRANCIARI TYPE GENERALIZED METRIC SPACES(Wolkite University, 2025-01-21) 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 situations.Item BEST PROXIMITY THEOREM FOR GENERALIZED (θ, γ)-PROXIMAL CONTRACTION MAPPING IN RECTANGULAR QUASI B- METRIC SPACE(Wolkite University, 2025-01-10) 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.Item A COMPARATIVE STUDY OF NUMERICAL METHODS FOR SOLVING SYSTEM OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS(Wolkite University, 2024-08-01) Gosa AshineIn this paper, three numerical methods are discussed to find the approximate solutions of a system of first order ordinary differential equations. Those are Classical Runge-Kutta method and Euler’s method. For each method formulas are developed for n systems of ordinary differential equations. The formulas explained by these methods are demonstrated by examples to identify the most accurate numerical methods. By comparing the analytical solution of the dependent variables with the approximate solution, absolute errors are calculated. The resulting value indicates that classical fourth order Runge-Kutta method offers most closet values with the computed analytical values. Finally, from the results the classical fourth order is more efficient method to find the approximate solutions of the systems of ordinary differential equationsItem NEW CONTRIBUTION IN BEST PROXIMITY POINT THEORY VIA AN AUXILIARY FUNCTION(Wolkite University, 2023-11-01) Abebu Getyein this thesis, we introduce the notion of proximal τ -distance contraction, proximal contractive and proximal T -contractive mappings. We establish best proximity point theorems, there by extending fixed point theory to the case of non self mapping and we prove the existence and uniqueness of a best proximity point for such types of mappings in a Hausdorff topological space. Examples are given to validate the main results.Item Common Best Proximity Point Theorems of Generalized Proximal (ψ, φ)-Weakly Contractive Mappings in b-Metric-Like spaces(Wolkite University, 2023-11-01) ABDREZAK AHMEDINIn this thesis, common best proximity point theorems for generalized proximal (ψ, φ)-weakly contractive mapping in the cases of non-self mappings are proved. We introduced the notion of generalized proximal (ψ, φ)-weakly contractive mappings in b-metric-like spaces and proved the existence and uniqueness of common best proximity point for generalized proximal (ψ, φ)- weakly contractive mappings in complete b-metric-like spaces. We also included one example supporting examples that our finding is more generalized with the references we used.Item COMMON BEST PROXIMITY POINT THEOREMS FOR GENERALIZED PROXIMAL WEAKLY CONTRATIVE MAPPING IN b-METRIC SPACES(Wolkite University, 2021-06-01) YITAGES NEGEDEIn this thesis, common best proximity point theorems for weakly contrac- tive mapping in b-metric spaces in the cases of non-self mappings are proved, we introduced the notion of generalized proximal weakly contrac- tive mappings in b-metric spaces and proved the existence and uniqueness of common best proximity point for these mappings in complete b-metric spaces. We also included some supporting examples that our finding is more generalize that the references we used.Item ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES(Wolkite University, 2021-08-01) Teka GidretaThis 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 IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCES SPECIALIZATION (ANALYSIS)(2021-08-01) DAGNAW TESHOMEThis Project will serve as a basic introduction to semigroups of linear operators. It will define a semigroup in the context of a physical problem which will serve to motivate further theoretical development of linear semigroups. Applications and examples will also be discussed.