We briefly summarize the results of thesis. We introduce and characterize character pseudo-amenability of Banach algebras A in terms of certain nets in A and show that both character amenability and pseudo-amenability of A are enough conditions for character pseudo-amenability of A but they are not a necessary conditions. We then describe character pseudo-amenability of the unitization of a Banach algebra. We show that character pseudo-amenability of a Banach algebra is equivalent to character pseudo-amenability of its unitization. We also investigate character pseudo-amenability of the second dual and the projective tensor product of Banach algebras In the sequel, we characterize character pseudo-amenability of A in terms of derivations from A into duals of certain Banach A-bimodules. For a locally compact group G, we study character pseudo-amenability of several Banach algebras related to G. Finally, we characterize character pseudo-amenability, character amenability and character contractibility of Segal algebras. We then give some applications of our results to Segal algebras on a locally compact group G.