I want to know about the ideas by which we can address the issues of 'credibility', 'authenticity', and 'fairness' in the analysis and presentation of qualitative data.
Try having a look at the edited book: issues of validity in qualitative research. And several others. There are quite many different appraches, but common to most of them is the idea that qualitative researchers - although (at least if they are non-positivist in their orientation) defying the notion of an objective reality must somehow still relate to the surrounding context. So validation is communicating your results to the social context you seek to portray and obtaining some feedback that suggest that these people feel themselves represented in your narrative.
I found that one of the articles that give quite a good overview is the following one: Barrett et al (2002): Verification strategies for establishing reliability and validity in qualitative research, International Journal of Qualitative Methods 1(2) (https://ejournals.library.ualberta.ca/index.php/IJQM/article/viewArticle/4603)- this does not concern data analysis directly but is more general, but it does portray some of the most important strategies qualitative researchers can use in order to ensure a high quality of their research, so it might be a good start for thinking about these issues or for any argumentation. Mind you though, the authors reject the idea of "member checks" as a valid method, so they contradict what Poul portrayed and which is widely used by qualitative researchers. It might just give you some interesting impulses. Hope it helps!
Personally I go for ensuring that all my data is properly coded and I use the start of open coding etc from grounded theory to ensure that my coding is good. I shall be publishing a book on Research Methods for PGs with Routledge later this year and i talk about to ensure credibility and validity of qualitative data in it.