Derivations on Banach algebras

The objective of this thesis is to make generalizations on module amenability, and to investigate the conditions to ensure that some types of derivations are stable in the sense of Hyers-Ulam-Rassias in Banach algebras. For this reason, some new notions have been introduced and some new properties have been obtained. The thesis mainly consists of six chapters. In the first chapter, short informations about some works which have been done in the literature related to amenability of Banach algebras and stability of some types of derivations have been given. In the second chapter, some basic definitions and properties which make easy reading of this thesis are given. In the third and fourth chapters, some important works have been done so far related to this subject are compiled to give an overview about the historical development of the topic of the thesis. In the fifth chapter, (σ)-n-weak module amenable Banach algebras have been introduced and obtained some new results about this notion. In the sixth chapter, Hyers-Ulam-Rassias stability of the k-th partial ternary quadratic derivations have been investigated in non-Archimedean Banach ternary algebras, and get some properties by using the fixed point method.