The development for coefficent inequality using any subclass in univalent function: a systematic literature review

Complex analysis involves studying the properties of complex number function. Geometric function theory is one of the fields for the complex analysis. A new generalized subclass of function is often implemented, and its characteristics are frequently discovered by researchers. However. With limited research and insufficient references, researchers find it challenging to generalize the subclasses of analytical functions that are currently in existence. The aim of this study was to determine the coefficient inequality using any subclass in a univalent function by carrying out a systematic literature review (SLR) using the PRISMA model. As SLR was done on articles obtained from these databases, data search was carried out using criteria developed from research using several search engines, including Google Scholar, Springer Link, Hindawi, Research Gate, and others. A total of 50 article were found, 25 of which were relevant to the objective of this work. Only 15 of the 25 article were relevant to the study. The results identified three major research themes, including the purpose of the study, type of subclass and properties. These results will probably serve as a framework for researchers, mathematicians, and university students to come up with a set of properties for determining coefficient inequality. The results of SLR opened a discussion on significant future study areas by identifying the main contributions, opportunities, and gaps in the discipline.