Abstract

A typical quandary in geometric functions theory is to study a functionalcomposed of amalgamations of the coefficients of the pristine function.Conventionally, there is a parameter over which the extremal value of thefunctional is needed. The present paper deals with consequential functional ofthis type. By making use of linear operator due to Hohlov \cite{6}, a newsubclass $\mathcal{R}_{a,b}^{c}$ of analytic functions defined in the open unitdisk is introduced. For both real and complex parameter, the sharp bounds forthe Fekete-Szeg\"{o} problems are found. An attempt has also been taken tofound the sharp upper bound to the second and third Hankel determinant forfunctions belonging to this class. All the extremal functions are express interm of Gauss hypergeometric function and convolution. Finally, the sufficientcondition 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.