Harandi Amini-Harandi [2012], in 2012 established the existence of a fixed point by using the concept of set-valued contraction. In the present paper, authors have generalized this concept by considering Hausdorff F-PGA contraction and assured the existence of a fixed point. Hence, it is interesting to note that in a complete Hausdorff metric space, the fixed point exists with a lighter contraction map. © Published under licence by IOP Publishing Ltd.