Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and basic (or q-) hypergeometric polynomials, are known to have widespread applications, particularly in several areas of number theory and combinatorial analysis such as (for example) the theory of partitions. Our usages here, in this survey-cum-expository article, of the q-calculus and the fractional q-calculus in geometric function theory of complex analysis are believed to encourage and motivate significant further developments on these and other related topics. By applying a fractional q-calculus operator, we define the subclasses $${\mathcal{S}}_{n}^{\alpha }(\lambda ,\beta ,b,q)$$ and $${\mathcal{G}}_{n}^{\alpha }(\lambda ,\beta ,b,q)$$ of normalized analytic functions with complex order and negative coefficients.
Among the results investigated for each of these function classes, we derive their associated coefficient estimates, radii of close-to-convexity, starlikeness and convexity, extreme points and growth and distortion theorems. Our investigation here is motivated essentially by the fact that basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several areas of number theory such as the theory of partitions. In fact, basic (or q-) hypergeometric functions are useful also in a wide variety of fields including, for example, combinatorial analysis, finite vector spaces, lie theory, particle physics, nonlinear electric circuit theory, mechanical engineering, theory of heat conduction, quantum mechanics, cosmology and statistics (see also (Srivastava and Karlsson in Multiple Gaussian hypergeometric series. pp 350–351, 1985) and the references cited thereon). In the last section on conclusion, we choose to point out the fact that the results for the q-analogues, which we consider in this article for $$0< q < 1$$, can easily (and possibly trivially) be translated into the corresponding results for the (p, q)-analogues (with $$0< q < p \leqq 1$$) by applying some obvious parametric and argument variations, the additional parameter p being redundant. Several other families of such extensively- and widely-investigated linear convolution operators as (for example) the Dziok–Srivastava, Srivastava–Wright and Srivastava–Attiya linear convolution operators, together with their extended and generalized versions, are also briefly considered.

Operators of Basic (or q-) Calculus and Fractional q-Calculus and Their Applications in Geometric Function Theory of Complex Analysis

Univalent functions, fractional calculus, and their applications , edited by H. M. Srivastava and S. Owa. Pp 404. £39·95. 1989. ISBN 0-7458-0701-1 (Ellis Horwood)

Some inclusion properties of a certain family of integral operators

The Concise Guide to PHARMACOLOGY 2017/18 provides concise overviews of the key properties of nearly 1800 human drug targets with an emphasis on selective pharmacology (where available), plus links to an open access knowledgebase of drug targets and their ligands (www.guidetopharmacology.org), which provides more detailed views of target and ligand properties. Although the Concise Guide represents approximately 400 pages, the material presented is substantially reduced compared to information and links presented on the website. It provides a permanent, citable, point-in-time record that will survive database updates. The full contents of this section can be found at http://onlinelibrary.wiley.com/doi/10.1111/bph.13884/full. Voltage-gated ion channels are one of the eight major pharmacological targets into which the Guide is divided, with the others being: G protein-coupled receptors, ligand-gated ion channels, other ion channels, nuclear hormone receptors, catalytic receptors, enzymes and transporters. These are presented with nomenclature guidance and summary information on the best available pharmacological tools, alongside key references and suggestions for further reading. The landscape format of the Concise Guide is designed to facilitate comparison of related targets from material contemporary to mid-2017, and supersedes data presented in the 2015/16 and 2013/14 Concise Guides and previous Guides to Receptors and Channels. It is produced in close conjunction with the Nomenclature Committee of the Union of Basic and Clinical Pharmacology (NC-IUPHAR), therefore, providing official IUPHAR classification and nomenclature for human drug targets, where appropriate.

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THE CONCISE GUIDE TO PHARMACOLOGY 2017/18: Voltage-gated ion channels

The purpose of the present paper is to introduce some new subclasses of strongly close-to-convex functions in the open unit disk defined by multiplier transformations and study their properties. Our results include several previous known results as special cases.

https://www.koreascience.or.kr:443/article/JAKO200311921892031.pdf

Jin-Lin Liu

Papers

A Linear Operator and Associated Families of Meromorphically Multivalent Functions

Classes of meromorphically multivalent functions associated with the generalized hypergeometric function

The Noor Integral and Strongly Starlike Functions

Certain properties of the Dziok-Srivastava operator

Subclasses of meromorphically multivalent functions associated with a certain linear operator