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In this paper, we employ a q -Noor integral operator to perform a q -analogue of certain fractional integral operator defined on an open unit disc. Then, we make use of the Hadamard convolution product to discuss several related results. Also, we derive a class of convex functions by utilizing the q -fractional integral operator and apply the inspired presented theory of the differential subordination, to geometrically explore the most popular differential subordination properties of the aforementioned operator. In addition, we discuss an exciting inclusion for the given convex class of functions. Over and above, we investigate the q -fractional integral operator and obtain some applications for the differential subordination. [ABSTRACT FROM AUTHOR]

Let A p n be the class of functions f z given by f z = z p + a p + n z p + n + a p + n + 1 z p + n + 1 + ⋯ which are analytic in the open unit disk U. For f z ∈ A p n , new integral operators O − j f z and O j f z j = 0 , 1 , 2 , ⋯. are considered. The operators O − j f z and O j f z satisfy O j O − j f z = O − j O j f z = f z and O − j ∗ O j f z = O j ∗ O − j f z = f ∗ f z for the convolution ∗ of O − j f z and O j f z. In the present paper, the dominants for both operators O − j f z and O j f z and subordinations for O − j f z and O j f z are discussed. Also, new subclass T p γ m , δ , ρ ; m , j concerning with m different boundary points is defined and discussed. Moreover, some interesting problems of T p γ m , δ , ρ ; m , j associated with O j f z are obtained. Furthermore, some interesting examples for our results are considered. [ABSTRACT FROM AUTHOR]

In this paper, we study some properties of analytic functions with fixed initial coefficients. The methodology of differential subordination is used for modification and improvements of several well-known results for subclasses of univalent functions by restricting the functions with fixed initial coefficients. Actually, by extending the Nunokawa lemma for fixed initial coefficient functions, we obtain some novel results on subclasses of univalent functions, such as differential inequalities for univalency or starlikeness of analytic functions. Also, we provide some new sufficient conditions for strongly starlike functions. The results of this paper extend and improve the previously known results by considering functions with fixed second coefficients. [ABSTRACT FROM AUTHOR]

In this paper we derive subordination and superordination results regarding the Atangana–Baleanu fractional integral applied to multiplier transformation and we give several differential sandwich-type theorems. Then, we apply the Atangana–Baleanu fractional integral to extended multiplier transformation on the class A ζ ∗ of normalized analytic functions and we derive strong differential subordination and strong differential superordination results regarding the extended new operator and we give the corresponding differential sandwich-type theorems from the first part of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a well known class studied by Ramesha in 1995 and later by Janteng in 2006, and we then extend the class to a wider class of functions f denoted by n α β , γ which are normalized and univalent, in the unit disk D = z ∈ ℂ : z < 1 satisfying the condition Re α z 2 f ′ ′ z / g z + z f ′ z / g z > β , 0 ≤ α < 1,0 ≤ β < 1 , where g is analytic function in D , such that g z ≠ 0 , with a new condition that is introduced. The main purpose of this paper is to give an estimate for the same a 3 − μ a 2 2 when f belongs to the class n α β , γ . [ABSTRACT FROM AUTHOR]

In this paper, we use the Faber polynomial expansion to obtain bounds for the general coefficients a n of bi-univalent functions in the family of analytic functions in the open unit disk. Estimation of the bound value for the initial coefficients of the functions in these classes is also established. [ABSTRACT FROM AUTHOR]

Aiming at the multiobjective topology optimization design of the structure, this paper proposes a method to establish the comprehensive objective function based on the normalized subobjective of the compromise programming method and to determine the weight coefficient of the subobjective of the comprehensive objective function by the analytic hierarchy process (AHP). By using statistical analysis and modal analysis, the static and dynamic characteristics of the gear can be obtained. The single objective topology optimization is used to reduce the compliance of the gear and elevate the low-order natural frequency, and the frequency weighting method is used to suppress the oscillation phenomenon in the frequency-single-objective optimization. AHP was used to determine the weight coefficient of each subtarget. The compromise programming method is used for multiobjective topology optimization, and the gear design is improved according to the optimization results. By analyzing the improved gear structure, the weight of the optimized gear is reduced by 25.3%. The overall stiffness performance and strength performance are enhanced, and the natural frequencies of each order are improved to different degrees. [ABSTRACT FROM AUTHOR]

In the case of passengers taking the subway many times in a short time, missing cards in and out of the station, and staying in the subway station for a long time, the previous table join method cannot accurately set the time threshold parameters and correctly match the OD pairs of passengers. In order to solve these problems, an OD matching method based on analysis function is proposed in this paper. LAG () is an analytic function in Oracle which allows you to access the row at a given offset prior to the current row without using a self-join. Metro IC card dataset stores the card swiping records of passengers entering and leaving the subway station every time. In this method, the dataset is sorted in ascending order according to the card number and card swiping time, and then, the lag function of Oracle is used to take the offset of the upper line of card ID, transaction date, transaction time, in and out sign, and station ID. Finally, the matching process is completed according to the OD conditions of card number, time, and inbound and outbound sign fields. This method does not need to set a time threshold and so as to deal with the situation where passengers stay too long in the subway station. The OD matching results on in and out IC swiping cards dataset in April and May 2019 of passengers of Xiamen Metro Line verify that analysis function method has better OD matching, missing swiping identification accuracy, and effect compared to the table join method. [ABSTRACT FROM AUTHOR]

This paper focuses on a two-dimensional completely resonant beam equation with a quintic nonlinear term. This means studying u t t + Δ 2 u + ε f u = 0 , x ∈ T 2 , t ∈ ℝ , under periodic boundary conditions, where ε is a small positive parameter and f u is a real analytic odd function of the form f u = f 5 u 5 + ∑ i ^ ≥ 3 f 2 i ^ + 1 u 2 i ∧ + 1 , f 5 ≠ 0. It is proved that the equation admits small-amplitude, Whitney smooth, linearly stable quasiperiodic solutions on the phase-flow invariant subspace ℤ † 2 = r = r 1 , r 2 , r 1 ∈ 4 ℤ − 1 , r 2 ∈ 4 ℤ . Firstly, the corresponding Hamiltonian system of the equation is transformed into an angle-dependent block-diagonal normal form by using symplectic transformation, which can be achieved by selecting the appropriate tangential position. Finally, the existence of a class of invariant tori is proved, which implies the existence of quasiperiodic solutions for most values of frequency vector by an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional Hamiltonian systems. [ABSTRACT FROM AUTHOR]

In this paper, using the basic concepts of symmetric q -calculus operator theory, we define a symmetric q -difference operator for m -fold symmetric functions. By considering this operator, we define a new subclass ℛ b φ , m , q of m -fold symmetric bi-univalent functions in open unit disk U. As in applications of Faber polynomial expansions for f m ∈ ℛ b φ , m , q , we find general coefficient a m k + 1 for n ≥ 4 , Fekete–Szegő problems, and initial coefficients a m + 1 and a 2 m + 1 . Also, we construct q -Bernardi integral operator for m -fold symmetric functions, and with the help of this newly defined operator, we discuss some applications of our main results. For validity of our result, we have chosen to give some known special cases of our main results in the form of corollaries and remarks. [ABSTRACT FROM AUTHOR]

A Stevi c ′ -Sharma operator denoted by T ψ 1 , ψ 2 , φ is a generalization product of multiplication, differentiation, and composition operators. In this paper, we characterize the bounded and compact Stevi c ′ -Sharma operator T ψ 1 , ψ 2 , φ from a general class X of Banach function spaces into Zygmund-type spaces with some of the most convenient test functions on the open unit disk. Using several restrictive terms, we show that all bounded operators T ψ 1 , ψ 2 , φ from X into the little Zygmund-type spaces are compact. As an application, we show that our results hold up for some other domain spaces of T ψ 1 , ψ 2 , φ , such as the Hardy space and the weighted Bergman space. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate and introduce several properties of certain families of analytic functions in the open unit disc, which are defined by q -analogue of Mittag-Leffler function associated with conic domain. A number of coefficient estimates of the functions in these classes have been obtained. Sufficient conditions for the functions belong to these classes are also considered. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an interesting class of analytic and biunivalent functions in the open unit disk Δ which is defined using the q -derivative operator. We apply the subordination method to the functional of coefficients problem. Furthermore, we obtain the bounds of the certain functional of coefficients for functions in the class H Σ q λ , β , for real and complex parameters. Also, an estimation for the initial Taylor and Maclaurin coefficients of functions in H Σ q λ , α was given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new subclasses of analytic functions in the open unit disc. Furthermore, the necessary and sufficient conditions for the Poisson distribution series to be in these new subclasses are found. [ABSTRACT FROM AUTHOR]

In this paper, we formulate the q -analogus of differential operator associated with q -Mittag-Leffler function. By using this newly defined operator, we define a new subclass k − U S q , γ m α , β , of analytic functions in conic domains. We investigate the number of useful properties such that structural formula, coefficient estimates, Fekete–Szego problem and subordination result. We also highlighted some known corollaries of our main results. [ABSTRACT FROM AUTHOR]

In the present paper, we will observe that the Sălăgean differential operator can be written in terms of Stirling numbers. Furthermore, we find a necessary and sufficient condition and inclusion relation for Pascal distribution series to be in the class ℙ k λ , α of analytic functions with negative coefficients defined by the Sălăgean differential operator. Also, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered. [ABSTRACT FROM AUTHOR]

In this paper, the 3IM+1CM theorem with a general difference polynomial L z , f will be established by using new methods and technologies. Note that the obtained result is valid when the sum of the coefficient of L z , f is equal to zero or not. Thus, the theorem with the condition that the sum of the coefficient of L z , f is equal to zero is also a good extension for recent results. However, it is new for the case that the sum of the coefficient of L z , f is not equal to zero. In fact, the main difficulty of proof is also from this case, which causes the traditional theorem invalid. On the other hand, it is more interesting that the nonconstant finite-order meromorphic function f can be exactly expressed for the case f ≡ − L z , f . Furthermore, the sharpness of our conditions and the existence of the main result are illustrated by examples. In particular, the main result is also valid for the discrete analytic functions. [ABSTRACT FROM AUTHOR]

The main objective of the present paper is to define a new subfamily of analytic functions using subordinations along with the newly defined q-Noor integral operator. We investigate a number of useful properties such as coefficient estimates, integral representation, linear combination, weighted and arithmetic means, and radius of starlikeness for this class. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate several inclusion relationships of new k -uniformly classes of analytic functions defined by the Mittag-Leffler function. Also, integral-preserving properties of these classes associated with the certain integral operator are also obtained. [ABSTRACT FROM AUTHOR]

All entire functions which transform a class of holomorphic Zygmund-type spaces into weighted analytic Bloch space using the so-called n -generalized superposition operator are characterized in this paper. Moreover, certain specific properties such as boundedness and compactness of the newly defined class of generalized integral superposition operators are discussed and established by using the concerned entire functions. [ABSTRACT FROM AUTHOR]

In the present paper, a subclass of analytic and biunivalent functions by means of Gegenbauer polynomials is introduced. Certain coefficients bound for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szegö problem for this subclass is solved. A number of known or new results are shown to follow upon specializing the parameters involved in our main results. [ABSTRACT FROM AUTHOR]

The main object of the present paper is to apply the concepts of p , q -derivative by establishing a new subclass of analytic functions connected with symmetric circular domain. Further, we investigate necessary and sufficient conditions for functions belonging to this class. Convex combination, weighted mean, arithmetic mean, growth theorem, and convolution property are also determined. [ABSTRACT FROM AUTHOR]

In this paper, a subspace T F 0 2,1 − s , s of the universal Teichmüller space, which is related to the analytic function space F 0 2,1 − s , s , is introduced and the holomorphy of the Bers map is shown. It is also proved that the pre-Bers map is holomorphic and the prelogarithmic derivative model T ˜ F 0 2,1 − s , s of T F 0 2,1 − s , s is a disconnected subset of the function space F 0 2,1 − s , s . Moreover, several equivalent descriptions of elements of T F 0 2,1 − s , s are obtained and the holomorphy of higher Bers maps is proved. [ABSTRACT FROM AUTHOR]

Harmonic functions can be constructed using two analytic functions acting as their analytic and coanalytic parts but the prediction of the behavior of convolution of harmonic functions, unlike the convolution of analytic functions, proved to be challenging. In this paper we use the shear construction of harmonic mappings and introduce dilatation conditions that guarantee the convolution of two harmonic functions to be harmonic and convex in the direction of imaginary axis. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class. [ABSTRACT FROM AUTHOR]

Data point overlap exists in the model translation recognition results of generalized maximum likelihood ratio detection (GLR) algorithm. A fuzzy semantic optimal control intelligent recognition model for English translation based on improved GLR algorithm is proposed. This algorithm is used to create a phrase corpus for marking tens of thousands of English and Chinese words, so that phrases can be searched automatically. The algorithm builds a phrase corpus of about 710,000 Chinese and English words. Phrase structure is constructed through phrase centers. Partial speech recognition results can be obtained. According to the syntactic function of analytic linear list, the ambiguity of Chinese and English structures in part of speech recognition results is corrected. Finally get the content of the identifier on the basis of comprehensive evaluation. The recognition accuracy based on the improved algorithm is more than 95%. The overall score was 92.3. This algorithm overcomes the disadvantages of GLR. Compared with statistical algorithm and dynamic memory algorithm, the algorithm improves the operation speed and processing performance and is more suitable for machine translation tasks. It provides a new idea in the field of machine translation. [ABSTRACT FROM AUTHOR]

This article deals with a classes of singular integral–differential equations with convolution kernel and reflection. By means of the theory of boundary value problems of analytic functions and the theory of Fourier analysis, such equations can be transformed into Riemann boundary value problems (i.e., Riemann–Hilbert problems) with nodes and reflection. For such problems, we propose a novel method different from classical one, by which the explicit solutions and the conditions of solvability are obtained. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of mild solutions for a class of fractional evolution equations with compact analytic semigroup. We prove the existence of mild solutions, assuming that the nonlinear part satisfies some local growth conditions in fractional power spaces. An example is also given to illustrate the applicability of abstract results. [ABSTRACT FROM AUTHOR]

Wulan et al. (2009), Wulan et al. characterized the compactness of composition operators on the Bloch space in the unit disk by the nth power of the induced analytic function. This paper will generalize the result to the Bloch type space in the polydisk. [ABSTRACT FROM AUTHOR]

Let P be the class of functions p(z) of the form ... which are analytic in the open unit disk ... . The object of the present paper is to derive certain argument inequalities of analytic functions p(z) in P. [ABSTRACT FROM AUTHOR]

For α, Γ ≥ 0 and ß < 1, let Wß(α, Γ) denote the class of all normalized analytic functions f in the open unit disc E = {z : |z| < 1} such that Reiɸ((1 - α + 2Γ)(f(z)/z)+ (α - 2Γ)f'(z)+ Γzf"(z) - ß) > 0, z ∈ E for some ɸ∈R. It is known (Noshiro (1934) and Warschawski (1935)) that functions in Wß(1, 0) are close-to-convex and hence univalent for 0 ≤ ß < 1. For f ∈ Wß(α, β), we consider the integral transform F(z) = Vλ(f)(z) := ...01λ (t)(f(tz)/t)dt, where λ is a nonnegative real-valued integrable function satisfying the condition ...01 (t)dt = 1. The aim of present paper is, for given ƍ < 1, to find sharp values of ß such that (i) Vλ(f) ∈ Wƍ(1, 0) whenever f ∈ Wß(α, Γ) and (ii) Vλ(f) ∈ Wƍ(α,Γ) whenever f ∈ Wß(α,Γ). [ABSTRACT FROM AUTHOR]

The present paper is concerned with the rational approximation of functions holomorphic on a domain G ⊂ C, having generalized types of rates of growth. Moreover, we obtain the characterization of the rate of decay of product of the best approximation errors for functions f having fast and slow rates of growth of the maximum modulus. [ABSTRACT FROM AUTHOR]

Let Γ denote the space of all entire sequences. Let Λ denote the space of all analytic sequences. In this paper, we introduce a new class of sequence space, namely, the semi-difference entire sequence space cs∩d1. It is shown that the intersection of all semi-difference entire sequence spaces cs∩d1 is I⊂cs∩d1 and Γ(Δ)⊂I [ABSTRACT FROM AUTHOR]

The object of the present paper is to introduce new classes of meromorphic functions with varying argument of coefficients defined by means of the Hadamard product (or convolution). Several properties like the coefficients bounds, growth and distortion theorems, radii of starlikeness and convexity, and partial sums are investigated. Some consequences of the main results for wellknown classes of meromorphic functions are also pointed out. [ABSTRACT FROM AUTHOR]

The main result in this paper is the determination of the Fréchet derivative of an analytic function of a bounded operator, tangentially to the space of all bounded operators. Some applied problems from statistics and numerical analysis are included as a motivation for this study. The perturbation operator (increment) is not of any special form and is not supposed to commute with the operator at which the derivative is evaluated. This generality is important for the applications. In the Hermitian case, moreover, some results on perturbation of an isolated eigenvalue, its eigenprojection, and its eigenvector if the eigenvalue is simple, are also included. Although these results are known in principle, they are not in general formulated in terms of arbitrary perturbations as required for the applications. Moreover, these results are presented as corollaries to the main theorem, so that this paper also provides a short, essentially self-contained review of these aspects of perturbation theory. [ABSTRACT FROM AUTHOR]

This paper gives some sufficient conditions for an analytic function to belong to the space consisting of all analytic functions f on the unit disk such lim∣a∣→1∫픻∣f'(z)∣²)q K (g(z, a)) dA(z) = 0. [ABSTRACT FROM AUTHOR]

This paper proposes a definition of generalized offsets for curves and surfaces, which have the variable offset distance and direction, by using the local coordinate system. Based on this definition, some analytic properties and theorems of generalized offsets are put forward. The regularity and the topological property of generalized offsets are simply given by representing the generalized offset as the standard offset. Some examples are provided as well to show the applications of generalized offsets. The conclusions in this paper can be taken as the foundation for further study on extending the standard offset. [ABSTRACT FROM AUTHOR]

In the paper by Mocanu (1980), Mocanu has obtained sufficient conditions for a function in the classes C¹ (U), respectively, and C²(U) to be univalent and to map U onto a domain which is starlike (with respect to origin), respectively, and convex. Those conditions are similar to those in the analytic case. In the paper by Mocanu (1981), Mocanu has obtained sufficient conditions of univalency for complex functions in the class C¹ which are also similar to those in the analytic case. Having those papers as inspiration, we try to introduce the notion of subordination for nonanalytic functions of classes C¹ and C² following the classical theory of differential subordination for analytic functions introduced by Miller and Mocanu in their papers (1978 and 1981) and developed in their book (2000). Let Ω be any set in the complex plane ℂ, let p be a nonanalytic function in the unit disc U, p ∈ C ² (U), and let ψ(r, s, t; z) : ℂ³ x U → ℂ. In this paper, we consider the problem of determining properties of the function p, nonanalytic in the unit disc U, such that p satisfies the differential subordination ψ (p(z), Dp(z), D²p(z) - Dp(z); z) ⊂ Ω ⇒ p(U) ⊂ Δ. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to deal with the shared values and uniqueness of analytic functions on annulus. Two theorems about analytic functions on annulus sharing four distinct values are obtained, and these theorems are improvement of the results given by Cao and Yi. [ABSTRACT FROM AUTHOR]

The one-parameter deformed exponential function was introduced as a frame that enchases a few known functions of this type. Such deformation requires the corresponding deformed operations (addition and subtraction) and deformed operators (derivative and antiderivative). In this paper, we will demonstrate this theory in researching of some functions defined by iterated deformed Laguerre operator. We study their properties, such as representation, orthogonality, generating function, differential and difference equation, and addition and summation formulas. Also, we consider these functions by the operational method. [ABSTRACT FROM AUTHOR]

By using a particular class of directional wavelets (namely, the conical wavelets, which are wavelets strictly supported in a proper convex cone in the k-space of frequencies), in this paper, it is shown that a tempered distribution is obtained as a finite sum of boundary values of analytic functions arising from the complexification of the translational parameter of the wavelet transform. Moreover, we show that for a given distribution f ∈ S′(ℝn), the continuous wavelet transform of f with respect to a conical wavelet is defined in such a way that the directional wavelet transform of f yields a function on phase space whose high-frequency singularities are precisely the elements in the analytic wavefront set of f. [ABSTRACT FROM AUTHOR]

Let R(픻) be the algebra generated in Sobolev space W22(픻) by the rational functions with poles outside the unit disk ̅픻. In this paper, we study the similarity invariant of the multiplication operators Mg in L(R(픻)), when g is univalent analytic on 픻 or Mg is strongly irreducible. And the commutants of multiplication operators whose symbols are composite functions, univalent analytic functions, or entire functions are studied. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to investigate several subordination- and superordination-preserving properties of a class of integral operators, which are defined on the space of analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also presented. Moreover, we consider an application of the subordination and superordination theorem to the Gauss hypergeometric function. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to derive some coefficient inequalities and subordination properties for certain subclasses of analytic functions involving the Salagean operator. Relevant connections of the results presented here with those obtained in earlier works are also pointed out. [ABSTRACT FROM AUTHOR]

Let Σ denote the class of analytic functions in the punctured unit disc u* = {z : 0 < |z| < 1}. Set φλ,lm,(z) = 1/z + Σk=0∞ [ l + λ(k + 1)/l]mzk (m ∈ N0;l > 0; λ ≥ 0; z ∈ u*), and define φ λ,lm,μ) in terms of the Hadamard product by φλ,lm,μ)(z) * φλ,lm,μ) (z) = 1/z(1 - z)μ (μ > 0; z ∈ u*). In this paper, we introduce several new subclasses of analytic functions defined by means of the operator Iμm (λ,l)ƒ(z) = φλ,lm,μ) (z) * ƒ(z) (ƒ ∈ Σ;m ∈ N0;l > 0; λ ≥ 0;μ > 0). Inclusion properties of these classes and some applications involving integral operator are also considered. [ABSTRACT FROM AUTHOR]

Both the forward and backward kinematics of the Gough-Stewart mechanism exhibit nonlinear behavior. It is critically important to take account of this nonlinearity in some applications such as path control in parallel kinematics machine tools. The nonlinearity of inverse kinematics is straightforward and has been first studied in this paper. However the nonlinearity of forward kinematics is more challenging to be considered as there is no analytic solution to the forward kinematic solution of the mechanism. A statistical approach including the Bates and Watts measures of nonlinearity has been employed to investigate the nonlinearity of the forward kinematics. The concept of standard sphere has been used to check the significance of the nonlinearity of the mechanism. It is demonstrated that the length of the region, defined as the linear approximation of the lifted line, has a significant impact on the nonlinearity of the mechanism. [ABSTRACT FROM AUTHOR]

In the case of the complex plane, it is known that there exists a finite set of rational numbers containing all possible growth orders of solutions of f(k) + ak-1(z)f(k-1) +…+a1(z)f' + a0(z)f = 0 with polynomial coefficients. In the present paper, it is shown by an example that a unit disc counterpart of such finite set does not contain all possible T- and M-orders of solutions, with respect to Nevanlinna characteristic and maximum modulus, if the coefficients are analytic functions belonging either to weighted Bergman spaces or to weighted Hardy spaces. In contrast to a finite set, possible intervals for T- and M-orders are introduced to give detailed information about the growth of solutions. Finally, these findings yield sharp lower bounds for the sums of T and M- orders of functions in the solution bases. [ABSTRACT FROM AUTHOR]

Let fn(z) = z + ∑Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. akzk be the sequence of partial sums of the analytic function f(z) = z + ∑ Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.akzk. In this paper, we determine sharp lower bounds for 핹{f'(z)/fn(z)},핹{fn(z)/f(z)}, 핹{f'(z)/fDue to image rights restrictions, multiple line equation(s) cannot be graphically displayed.(z)}, and 핹{fDue to image rights restrictions, multiple line equation(s) cannot be graphically displayed.(z)/f'(z)}. The usefulness of the main result not only provides the unification of the results discussed in the literature but also generates certain new results. [ABSTRACT FROM AUTHOR]

We introduce a new subclass of meromorphically analytic functions, which is defined by means of a Hadamard product (or convolution). A characterization property such as the coefficient bound is obtained for this class. The other related properties, which are investigated in this paper, include the distortion and the radius of starlikeness. We also consider several applications of our main results to the generalized hypergeometric functions. [ABSTRACT FROM AUTHOR]

For α≥0, λ>0, we consider the M(α,λ)b of normalized analytic α-λ convex functions defined in the open unit disc U. In this paper, we investigate the class M(α,λ)b, that is, Re{(zfb′(z)/fb(z))[1-α+α(1-λ)(zfb′(z)/fb(z))+αλ(1+(zfb′′(z)/fb′(z)))]}>0, with fb is Koebe type, that is, fb(z):=z/(1-zn)b. The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class M(α,λ)b of n-fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated. [ABSTRACT FROM AUTHOR]