Some geometric properties of multivalent functions associated with a new generalized $ q $-Mittag-Leffler function

Abstract

<abstract><p>In this article, a new generalized $ q $-Mittag-Leffler function is introduced and investigated. Motivated by the newly defined function and using the concept of differential subordination, a new subclass of multivalent functions is introduced. Some geometric properties of them are obtained. Furthermore, the radii for the aforementioned subclass associated with a generalized Srivastava-Attiya integral operator are also studied.</p></abstract>

New Class of Multivalent Functions with Negative Coefficients

“…We find that <;( )= x7 = v @ ( + 1) − ( + )(1 + v − ) @ ( + 1) − ( + )(1 + − ) 7 , ∞ that yield easily ;(0) = 0.…”

“…Upon choosing the values of on the positive real axis where 0 ≤ = V < 1, ,-<−-PQ = ≥ −U-PQ U = −1 and letting V → 1 7 , we conclude to (2.4) by using (2.1) in left hand of (2.4).…”

Sandwich-Type Theorems for a Family of Non-Bazilevič Functions Involving a q-Analog Integral Operator

“…The q-calculus idea, which includes the q-derivative and q-integral, was first proposed by Jackson ([17,18]). As the study of q-calculus has expanded, various related topics have been investigated, including the q-Gamma function, the q-Beta function, and the q-Mittag-Leffler function (for further information, refer to [19][20][21][22]). In the field of GFT, the application of q-calculus has been effective in studying classes of functions, including S and S(p).…”

Bi-univalent functions of order ζ connected with ( m , n ) -Lucas polynomials

“…Recently, numerous studies have examined certain classes analytic functions in U utilizing fractional q-calculus operators. In the present paper, some parts of the q-calculus theory will be employed to reach our results: see the following papers for more information on the notions of q-calculus ( [4,17,20,22,23,34,37]).…”