We introduce a subclass k - T US∗(α, ϑ)of uniformly starlike functions fand study characterization theorem and coefficients estimates. We also define a neighbourhood of a function funder certain assumptions and study this neighborhood related results. We establish results relating to the partial sums of functions belonging to the class k - T US∗(α, ϑ). These functions are closely linked with the conformal mappings which lead to the growing applications in boundary and eigen-value problems in mathematics and various other fields of science and engineering. This research may also be related with the various
known classes already found in the literature.