University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Bounded Approximate Character Amenability of Banach Algebras1071183543510.22130/scma.2018.79315.372ENHasanPourmahmood AghababaDepartment of Mathematics, University of Tabriz, Tabriz, Iran.FouroghKhedriDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.Mohammad HosseinSattariDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.Journal Article20180115The bounded approximate version of $varphi$-amenability and character amenability are introduced and studied. These new notions are characterized in several different ways, and some hereditary properties of them are established. The general theory for these concepts is also developed. Moreover, some examples are given to show that these notions are different from the others. Finally, bounded approximate character amenability of some Banach algebras related to locally compact groups are investigated.http://scma.maragheh.ac.ir/article_35435_9d883ba7e3298bfb19d2cc5f830fe1a2.pdf