On regularity of ?1, ?2 near-rings

This thesis consists of five chapters. The literature and basic informations about the study have been given in the first and second chapters. In the third chapter, the relations of ?1 and ?2 near-ring concepts with each other and regular near-rings have been examined. In the fourth chapter, the relations of the concepts of bi-idealness, bi-regularness in near-rings with a lot of different near-ring kinds have been investigated.In the fifth chapter, which consists of an original study, various relations of ?1 near-rings with regular near-rings have been obtained. Furthermore, ?1 subnear-ring of a near-ring has been defined and its various propertics have been proved. The features of ?1 and ?2 subnear-rings have been researched under near-ring homomorphism.