Could we combine the research with mixed method between a qualitative approach in case study method and study literature review?

Yes, it is possible to combine a qualitative approach through the case study method and a study literature review in mixed methods research design. In this case, the qualitative approach through the case study method can provide in-depth insights into a particular phenomenon or context, while the study literature review can provide a broader perspective and context for the research question. By combining these two methods in a mixed methods design, the research can benefit from the strengths of both methods and provide a more holistic and nuanced understanding of the research question. When designing a mixed methods research design , it is important to carefully plan and integrate the different methods and techniques used to effectively address the research question and ensure their compatibilities, such as ensuring that the research question aligns with the objectives of both the case study and literature review.

Mixed methods requires the integration of the results from a qualitative study and a quantitative study. I personally would not consider a literature review to be a quantitative study.

You may refer to the below article regarding this issue-

David is correct here. Ariful - the example that you provide commences with a literature review and then qualitative interviews. For me, this would make more sense than the other way around. The article, correctly, does not refer to its methodology as mixed methods.

Research methodology is data collection, analysis, interpretation through qualitative or quantitative or combination of both including triangulation methods. Where by case studies are the application in any organization- small or big. If organizations are very big, we can get data from the one are similar organizations to test our hypotheses, in case we want to check industry wide performance etc, we can apply the methods. The qualitative or quantitative or combination of both including triangulation methods can be used. These method can be also used in empirical researches as well. On the other hand 'literature reviews' are to help researchers to identify 'Research Gap' and to develop theoretical or conceptual framework to explain IDV, DV and MV to put the research or your study on track and at least relevant.