The q-difference operator associated with the multivalent function bounded by conical sections

C Ramachandran,Basem Frasin,S Annamalai

doi:10.5269/bspm.32913

Abstract

In this paper we obtain some inclusion relations of k - starlike functions, k - uniformly convex functions and quasi-convex functions. Furthermore, we obtain coe¢ cient bounds for some subclasses of fractional q-derivative multivalent functions together with generalized Ruscheweyh derivative.

Highlights

We note that UCC(0, α, β) is the class of close-to-convex of univalent functions of order α and type β and UQC(0, α, β) is the class of quasi-convex univalent functions of order α and type β
Special relativity applies to elementary particles and their interactions, whereas general relativity applies to the cosmological and astrophysical realm, including astronomy
In our q-difference operator plays an vital role in the theory of hypergeometric series and quantum physics

Summary

Preliminaries

The theory of relativity, or relativity in physics, usually encompasses two theories by Albert Einstein: special relativity and general relativity. Let f be a function defined on a q-geometric set. [20] The fractional q-integral operator Iqδ,z of a function f (z) of order δ(δ > 0) is defined by z. [20] The fractional q-integral operator Dqδ,z of a function f (z) of order δ(0 ≤ δ < 1) is defined by z. Under the Definition 2.6, the The fractional q-derivative for a function f (z) of order δ is defined by. The q-differ-integral operator Ωδq,p : Ap → Ap, for δ < p + 1, 0 < q < 1 and n ∈ N, defined as follows: Ωδq,p. Let Qk,α(z) be a univalent starlike function with respect to 1 which maps the open unit disk U onto a region in the conical domain and is symmetric with respect to the real axis, Qk,α(0) = p, Q′k,α(0) > 0.

Inclusion Relation Problems

A BpbQ21