On ulam type stabilities of some impulsive differential equations

This master's thesis is composed of eight sections. Chapter one is presented as "Introduction". This chapter provides brief information about the significance of the thesis topic within the scientific literature and the emergence of Ulam stability. The second chapter is titled "Literature Review". In this chapter, some studies related to the thesis topic in the relevant literature are presented in summary form. The third chapter, titled "Materials and Methods" includes brief information about the materials used in this thesis, together with the approaches and procedures applied in proving the results presented. The fourth chapter of the thesis is presented under the title "Some Basic Definitions and Theorems Related to Impulsive Differential Equations". This chapter includes the definition of impulsive differential equations, the concept of solutions for such equations, basic properties of solutions, results concerning existence and uniqueness and examples related to impulsive differential equations. The fifth chapter is titled "UHR Stability for an Ordinary Impulsive Differential Equation". In this chapter, some results regarding the UHR stability of a first order ordinary impulsive differential equation is presented.The sixth chapter is titled "UHR Stability of Semilinear Differential Impulsive Equation". In this chapter, the Ulam-type stability of some semilinear differential impulsive equations are examined. The seventh chapter of the thesis is presented under the title "UHR Stability of an Ordinary Differential Equation in a Banach Space" and it investigates the UHR stability of the given differential equation within a Banach space using the generator of a semigroup. Finally, the eighth chapter is titled "UHR Stability for a First-Order Impulsive Evolution Equation." In this chapter, some similar results as in the previous chapters on the Ulam-type stability with respect to the considered equation are provided.