Conic Regions Research Articles

On a characterization of starlike functions with respect to (2ȷ,ℓ)-symmetric conjugate points

In this paper, we introduce and study a new subclass of starlike functions with respect to [Formula: see text]-symmetric conjugate points using the principle of subordination. Several relationship with the well-known classes have been established. We have focussed on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of the results are presented here as corollaries, most of which are extensions of well-known results.

Classes of Multivalent Spirallike Functions Associated with Symmetric Regions

We define a function to unify the well-known class of Janowski functions with a class of spirallike functions of reciprocal order. We focus on the impact of defined function on various conic regions which are symmetric with respect to the real axis. Further, we have defined a new subclass of multivalent functions of complex order subordinate to the extended Janowski function. This work bridges the studies of various subclasses of spirallike functions and extends well-known results. Interesting properties have been obtained for the defined function class. Several consequences of our main results have been pointed out.

Bazilevič Functions of Complex Order with Respect to Symmetric Points

In this paper, we familiarize a class of multivalent functions with respect to symmetric points related to the differential operator and discuss the impact of Janowski functions on conic regions. Inclusion results, the subordination property, and coefficient inequalities are obtained. Further, the applications of our results that are extensions of those given in earlier works are presented as corollaries.

Subclass of analytic functions involving Erdély–Kober type integral operator in conic regions and applications to neutrosophic Poisson distribution

In this article we familiarize a new subclass of analytic functions comprising Erdély–Kober type integral operator linked with the Janowski functions. Further, we confer some significant geometric properties like necessary and sufficient condition, growth and distortion bounds convex combination, partial sums and Fekete–Szegő inequality for this newly demarcated class. Further we conferred Fekete–Szegő inequality related with neutrosophic Poisson distribution.

Applications of Symmetric Conic Domains to a Subclass of q-Starlike Functions

In this paper, the theory of symmetric q-calculus and conic regions are used to define a new subclass of q-starlike functions involving a certain conic domain. By means of this newly defined domain, a new subclass of normalized analytic functions in the open unit disk E is given. Certain properties of this subclass, such as its structural formula, necessary and sufficient conditions, coefficient estimates, Fekete–Szegö problem, distortion inequalities, closure theorem and subordination results, are investigated. Some new and known consequences of our main results as corollaries are also highlighted.

Starlike Functions of Complex Order with Respect to Symmetric Points Defined Using Higher Order Derivatives

In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries.

Properties of $ \lambda $-pseudo-starlike functions with respect to a boundary point

<abstract><p>The purpose of this present paper is to investigate some mapping properties of functions which map the unit disc onto a overlapped leaf-like curve, having real part greater than zero. Also we define a class of $ \lambda $-pseudo starlike functions related to a leaf-like curve. Integral representation, inequalities for the initial Taylor-Maclaurin coefficients and Fekete-Szegö problem for subclasses of analytic functions related to various conic regions are obtained as our main results.</p></abstract>

On q‐Convex Functions Defined by the q‐Ruscheweyh Derivative Operator in Conic Regions

The core objective of this article is to introduce and investigate a new class of convex functions associated with the conic domain defined by the Ruscheweyh q‐differential operator. Many interesting properties such as sufficiency criteria, coefficient bounds, partial sums, and radius of convexity of order α for the functions of the said class are investigated here.

Design and analysis of a Contact-Aided Leaf Hinge (CALH) with continuous variable stiffness

This paper introduces a design method to realize the transition of variable stiffness from discrete to continuous through contact interaction. Based on this, a Contact-Aided Leaf Hinge (CALH) with passive variable stiffness is proposed, which consists of a flexible segment and a rigid part. As the deformation increases, the flexible segment contacts with the rigid part continuously, resulting in the variation of bending stiffness. The configuration, modeling and deformation process are illustrated in detail. Several examples of conic contact regions are analyzed through the chained pseudo-rigid-body model (CPRBM) and finite element analysis (FEA). Besides, physical prototypes are manufactured and experimental tests are performed to verify the feasibility of the design. Finally, some applications, parasitic motion and coupling effects are discussed. By further designing the dimensions and contact surface, the CALH can satisfy various requirements.

Properties of λ-Pseudo-Starlike Functions of Complex Order Defined by Subordination

In this paper, we defined a new class of λ-pseudo-Bazilevič functions of complex order using subordination. Various classes of analytic functions that map unit discs onto a conic domain and some classes of special functions were studied in dual. Some subordination results, inequalities for the initial Taylor–Maclaurin coefficients and the unified solution of the Fekete–Szegő problem for subclasses of analytic functions related to various conic regions, are our main results. Our main results have many applications which are presented in the form of corollaries.

A Subclass of q-Starlike Functions Defined by Using a Symmetric q-Derivative Operator and Related with Generalized Symmetric Conic Domains

In this paper, the concepts of symmetric q-calculus and conic regions are used to define a new domain Ωk,q,α˜, which generalizes the symmetric conic domains. By using the domain Ωk,q,α˜, we define a new subclass of analytic and q-starlike functions in the open unit disk U and establish some new results for functions of this class. We also investigate a number of useful properties and characteristics of this subclass, such as coefficients estimates, structural formulas, distortion inequalities, necessary and sufficient conditions, closure and subordination results. The proposed approach is also compared with some existing methods to show the reliability and effectiveness of the proposed methods.

The nearest polyhedral convex conic regions for high-dimensional classification

In the nearest-convex-model type classifiers, each class in the training set is approximated with a convexclass model, and a test sample is assigned to a class based on the shortest distance from the test sample to these classmodels. In this paper, we propose new methods for approximating the distances from test samples to the convex regionsspanned by training samples of classes. To this end, we approximate each class region with a polyhedral convex conicregion by utilizing polyhedral conic functions (PCFs) and its extension, extended PCFs. Then, we derive the necessary formulations for computing the distances from test samples to these new models. We tested the proposed methodson different high-dimensional classification tasks including face, digit, and generic object classification as well as onsome lower-dimensional classification problems. The experimental results on different datasets show that the proposedclassifiers achieve either the best or comparable results on high-dimensional classification problems compared to othernearest-convex-model classifiers, which shows the superiority of the proposed methods.

Properties of New Holomorphic Mappings with Respect to Conic Domains

This paper is mainly about holomorphic mappings associated with conic regions which are closely connected with k — ST(α). We introduce new subclasses of starlike (spirallike) functions, namely, S (k,α)(S (k,α,β)), and discuss their coefficient estimates and the Fekete-Szego-Goluzin’s problem. Then we generalize S (k,α,β) on the unit ball Bn in ℂn, that is, k-conic spirallike mappings of type β and order α. We obtain the growth, covering and distortion theorems of the generalized mappings. Besides that, we construct k-conic spirallike mappings of type β and order α on Bn through Sc(k,α,β) by the generalized Roper-Suffridge extension operators.

On Certain Generalized Bazilevic type Functions Associated with Conic Regions

Let $f$ and $g$ be analytic in the open unit disc and, for $alpha ,$ $beta geq 0$, letbegin{align*}Jleft( alpha ,beta ,f,gright) & =frac{zf^{prime }(z)}{f^{1-alpha}(z)g^{alpha }(z)}+beta left( 1+frac{zf^{prime prime }(z)}{f^{prime}(z)}right) -beta left( 1-alpha right) frac{zf^{prime }(z)}{f(z)} \& quad -alpha beta frac{zg^{prime }(z)}{g(z)}text{.}end{align*}The main aim of this paper is to study the class of analytic functions which map $Jleft( alpha ,beta ,f,gright) $ onto conic regions. Several interesting problems such as arc length, inclusion relationship, rate of growth of coefficient and Growth rate of Hankel determinant will be discussed.

On Janowski Close-to-Convex Functions Associated with Conic Regions

In this work, we introduce and investigate a class of analytic functions which is a subclass of close-to-convex functions of Janowski type and related to conic regions. Length of the image curve |z| = r < 1 under the generalized Janowski close-to-convex function is derived. Furthermore, rate of growth of coefficients and Hankel determinant for this class are obtained. Relevant connections of our results with the earlier known results are also pointed out.

New subclass of <i>q</i>-starlike functions associated with generalized conic domain

In this paper, the concepts of quantum (or q-) calculus and conic regions are combined to define a new domain Ωk, q, γ which represents the generalized conic regions. Then by using a certain generalized conic domain Ωk, q, γ we define and investigate a new subclass of normalized analytic functions in open unit disk E. We also investigate a number of useful properties and characteristics of this subclass such as, structural formula, necessary and sufficient condition, coefficient estimates, Feketo-Szego problem, distortion inequalities, closure theorem, and subordination result. We also highlight some known consequences of our main results as corollaries.

Inclusion relations for certain families of integral operators associated with conic regions

In this work, we introduce certain subclasses of analytic functions involving the integral operators that generalize the class of uniformly starlike, convex, and close-to-convex functions with respect to symmetric points. We then establish various inclusion relations for these newly defined classes.

On Generalized Bounded Mocanu Variation Related to q-Derivative and Conic Regions

On Generalized Bounded Mocanu Variation Related to q-Derivative and Conic Regions

Starlike and convex functions with respect to symmetric conjugate points involving conical domain

AbstractEnough attentions to domains related to conical sections has not been done so far although it deserves more. Making use of the conical domain the authors have defined a new class of starlike and Convex Functions with respect to symmetric points involving the conical domain. Growth and distortion estimates are studied with convolution using domains bounded by conic regions. Certain coefficient estimates are obtained for domains bounded by conical region. Finally interesting application of the results are also highlighted for the function Ωk,βdefined by Noor.

Janowski type close-to-convex functions associated with conic regions

The analytic functions, mapping the open unit disk onto petal and oval type regions, introduced by Noor and Malik (Comput. Math. Appl. 62:2209-2217, 2011), are considered to define and study their associated close-to-convex functions. This work includes certain geometric properties like sufficiency criteria, coefficient estimates, arc length, the growth rate of coefficients of Taylor series, integral preserving properties of these functions.