  A typical quandary in geometric functions theory is to study a functional
composed of amalgamations of the coefficients of the pristine function.
Conventionally, there is a parameter over which the extremal value of the
functional is needed. The present paper deals with consequential functional of
this type. By making use of linear operator due to Hohlov \cite{6}, a new
subclass $\mathcal{R}_{a,b}^{c}$ of analytic functions defined in the open unit
disk is introduced. For both real and complex parameter, the sharp bounds for
the Fekete-Szeg\"{o} problems are found. An attempt has also been taken to
found the sharp upper bound to the second and third Hankel determinant for
functions belonging to this class. All the extremal functions are express in
term of Gauss hypergeometric function and convolution. Finally, the sufficient
condition for functions to be in $\mathcal{R}_{a,b}^{c}$ is derived.
  Relevant connections of the new results with well known ones are pointed out.
