On certain subclasses of multivalent functions with varying arguments of coefficients

In this paper we introduce and study new classes VM_{p,η}(λ,α,β) and VN_{p,η}(λ,α,β) of multivalent functions with varying arguments of coefficients. We obtain coefficients inequalities, distortion theorems and extreme points for functions in these classes. Also, we investigate several distortion inequalities involving fractional calculus. Finally, results on partial sums are considerd.

Applications on a subclass of β-uniformly starlike functions connected with q-Borel distribution

The aim of this paper is to define the operator of [Formula: see text]-derivative based upon the Borel distribution and by using this operator, we familiarize a new subclass of [Formula: see text]-uniformly starlike functions [Formula: see text]-[Formula: see text] Further, we obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions [Formula: see text]-[Formula: see text] We also determine the second Hankel inequality for functions belonging to this subclass.

Certain Classes of Analytic Functions Bound with Kober Operators in q -Calculus

Through applying the Kober fractional q -calculus apprehension, we preliminary implant and introduce new types of univalent analytical functions with a q -differintegral operator in the open disk U = ξ ∈ ℂ : ∣ ξ | < 1 . The coefficient inequality and distortion theorems are among the results examined with these forms of functions. Specific cases are responded and addressed immediately. The findings include an expansion of the numerous established results in the q -theory of analytical functions.

Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

Applications of Certain Conic Domains to a Subclass of q-Starlike Functions Associated with the Janowski Functions

In our present investigation, with the help of the basic (or q-) calculus, we first define a new domain which involves the Janowski function. We also define a new subclass of the class of q-starlike functions, which maps the open unit disk U, given by U= z:z∈C and z <1, onto this generalized conic type domain. We study here some such potentially useful results as, for example, the sufficient conditions, closure results, the Fekete-Szegö type inequalities and distortion theorems. We also obtain the lower bounds for the ratio of some functions which belong to this newly-defined function class and for the sequences of the partial sums. Our results are shown to be connected with several earlier works related to the field of our present investigation. Finally, in the concluding section, we have chosen to reiterate the well-demonstrated fact that any attempt to produce the rather straightforward (p,q)-variations of the results, which we have presented in this article, will be a rather trivial and inconsequential exercise, simply because the additional parameter p is obviously redundant.

Classes of harmonic functions defined by extended Sălăgean operator

UDC 517.57 The object of the present paper is to investigate classes of harmonic functions defined by the extended Sălăgea operator. By using the extreme points theory we obtain coefficients estimates and distortion theorems for these classes of functions. Some integral mean inequalities are also pointed out.

Applications of $ q $-difference symmetric operator in harmonic univalent functions

<abstract><p>In this paper, for the first time, we apply symmetric $ q $ -calculus operator theory to define symmetric Salagean $ q $-differential operator. We introduce a new class $ \widetilde{\mathcal{H}}_{q}^{m}\left(\alpha \right) $ of harmonic univalent functions $ f $ associated with newly defined symmetric Salagean $ q $-differential operator for complex harmonic functions. A sufficient coefficient condition for the functions $ f $ to be sense preserving and univalent and in the same class is obtained. It is proved that this coefficient condition is necessary for the functions in its subclass $ \overline{\widetilde{\mathcal{H}}_{q}^{m}\left(\alpha \right) } $ and obtain sharp coefficient bounds, distortion theorems and covering results. Furthermore, we also highlight some known consequence of our main results.</p></abstract>

A Study of Some Families of Multivalent q-Starlike Functions Involving Higher-Order q-Derivatives

In the present investigation, by using certain higher-order q-derivatives, the authors introduce and investigate several new subclasses of the family of multivalent q-starlike functions in the open unit disk. For each of these newly-defined function classes, several interesting properties and characteristics are systematically derived. These properties and characteristics include (for example) distortion theorems and radius problems. A number of coefficient inequalities and a sufficient condition for functions belonging to the subclasses studied here are also discussed. Relevant connections of the various results presented in this investigation with those in earlier works on this subject are also pointed out.

Properties of a New Subclass of Analytic Functions With Negative Coefficients Defined by Using the Q-Derivative

In this paper we define a new class of analytic functions with negative coefficients involving the q-differential operator. Our main purpose is to determine coefficient inequalities and distortion theorems for functions belonging to this class. Connections with previous results are pointed out.