UPPER BOUNDS FOR RADIUS PROBLEMS INVOLVING RATIOS OF ANALYTIC FUNCTIONS

. In recent years, the problem of finding the sharp radii bounds for certain properties in geometric function theory has attracted several researchers. However, there are several instances where only lower bounds for the radius problems have been established. In this paper, we have worked in a similar direction to compute the upper bounds in these cases which coincides with the conjectured values. Moreover, explicit functions are provided which yield that these bounds are attainable.