Hyers-ulam stability and hyers-ulam-rassias stability in some models of integral and integro-differential equations

This thesis consists of eight chapters. In the first chapter of the thesis, background information with regard to the subject of the thesis is given. In Chapter 2 of this thesis, literature review, i.e. some works related to subject of the thesis are briefly summarized. In Chapter 3 of the thesis, the materials and methods used in the thesis are noted, and as basic information, some background definitions, the theorems, a lemma, etc., which are related to the subject of the thesis, are given. In Chapter 4 of thesis, the Hyers-Ulam stability of a nonlinear integro-differential equation and an integral equation are investigated. In Chapter 5 of the thesis, the Hyers-Ulam and Hyers-Ulam-Rassias stability of a Volterra-integro differential equation with a variable delay is discussed and some examples are give as applications of the results. In Chapter 6 of the thesis, the Hyers-Ulam and Hyers-Ulam-Rassias stability of a nonlinear Volterra-integro differential equation with a variable delay is investigated. In particular cases, examples are provided for illustrations. In Chapter 7 of the thesis, the Hyers-Ulam and Hyers-Ulam-Rassias stability of a nonlinear Volterra-integro differential equation are presented. In particular cases, two examples are presented for illustrations. The last chapter includes the discussion and conclusion of the work we have done in this thesis.