Using the real parameters λ and τ with −1 ≤ τ < λ < 1, a generalized q −extension of the function in , is defined. The function is then used as a subordination function to construct a novel subclass; of q −starlike functions. Various special forms of this class are discussed and are being linked to a previously defined family of certain q −starlike functions. In addition, for functions belonging to the said class; coefficient estimates, Fekete–Szegö inequality, necessary and sufficient conditions are investigated.

Let R be an associative ring with identity. In this paper we extend the J.H. Maynes results, which he treatised in [28]. In particular, we prove that if R is a δ-prime ring with charR non equal 2 and I is a nonzero δ-ideal of R, where δ ∈ D, c ∈ R and [c, δ(c)] in the center of R, then R is commutative.

Let R be an associative and 2-torsion-free ring with an identity. in this work, we will generalize the results of differentially prime rings in [18] by applying the hypotheses in a differentially semiprime rings. In particular, we have proved that if R is a D-semiprime ring, then either R is a commutative ring or D is a semiprime ring.