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The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on the properties of the differential subordination and superordination one of the newest techniques used in this field, we obtain some differential subordination and superordination results for multivalent functions defined by differintegral operator with j -derivatives ℑ p (ν , ρ ; ℓ) f (z) for ℓ > 0 , ν , ρ ∈ R , such that (ρ − j) ≥ 0 , ν > − ℓ p (p ∈ N) in the open unit disk U . Differential sandwich result is also obtained. Also, the results are followed by some special cases and counter examples. The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on the properties of the differential subordination and superordination one of the newest techniques used in this field, we obtain some differential subordination and superordination results for multivalent functions defined by differintegral operator with -derivatives for such that in the open unit disk . Differential sandwich result is also obtained. Also, the results are followed by some special cases and counter examples. [ABSTRACT FROM AUTHOR]

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We prove some combinatorial identities by an analytic method. We use the property that singular integrals of particular functions include binomial coefficients. In this paper, we prove combinatorial identities from the fact that two results of the particular function calculated as two ways using the residue theorem in the complex function theory are the same. These combinatorial identities are the generalization of a combinatorial identity that has been already obtained. [ABSTRACT FROM AUTHOR]

The class B¯ B(α) of non-Bazilevič functions was introduced by Obradović. Later, estimates on the second coefficient and Fekete-Szegö functional for normalized analytic functions in the class B¯ B(α) were investigated by Tuneski and Darus. In the present work, sharp estimate on third to eighth coefficients for normalized analytic functions f(z) = z + a2z2 + a3z3 + … ∊ B¯(α) are investigated. Further sharp estimate on the functional ®a2a3 - a4® is also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of analytic functions associated with Mittag-Leffler fuction in the open unit disk. Several properties of functions belonging to this class are derived. [ABSTRACT FROM AUTHOR]

The main object of this article is to define a new class of analytic functions using q - Sãlãgean differential operator involving complex order. We obtain coefficient estimates and other useful properties for this new class. [ABSTRACT FROM AUTHOR]

Given an analytic standardly normalized function g in D := {z ∊ C : ∣z∣ < 1}, by C(g) will be denoted the class of analytic standardly normalized function f such that Re {eiδzf'(z)/g(z)}>0, z ∊ D, for some δ ∊ (-π/2, π/2). For the class C(g) the Fekete-Szegö problem is examined. [ABSTRACT FROM AUTHOR]

In this paper, we define certain subclasses of analytic univalent function associated with quasi-subordination. Some results such as coefficient bounds and Fekete-Szego bounds for the functions belonging to these subclasses are derived. [ABSTRACT FROM AUTHOR]

In this paper we consider two types of harmonic mappings w(z) ∊ SH(D, Ω1) and w(z) ∊ SH(픻,R), where 픻 is the unit disk and Ω1, R are the domain defined by (2) and (3). Using the representation of harmonic mappings, we find the sufficient and necessary conditions to make w(z) be a harmonic quasiconformal mapping. Furthermore, we obtain some estimates of w(z). [ABSTRACT FROM AUTHOR]

The purpose of this study is to investigate the effects of using geometric functions approach on 9th grade students' motivation levels toward mathematics in functions unit. Participants of this study were 87 students who were ongoing in the first year of high school in Turkey. In this research, pretest and posttest control group quasiexperimental design was used. In the experimental group I, geometric functions approach and dynamic mathematics software which supported the mathematics teaching were used. In the experimental group II, dynamic mathematics software which supported the mathematics teaching was used. In the control group, traditional mathematics teaching method was used as a teaching method. The data of this study were collected by Students' Motivation toward Mathematics Learning questionnaire (SMTML). Before the experimental process, there was no statistically significant difference between students' motivation levels toward mathematics. After the experimental process, there was not a significant difference between experimental group I, experimental group II and control groups except for achievement goal dimension post-test scores. In achievement goal dimension there was a statistically significant difference between groups. The results of this study indicate that using geometric functions approach in the learning process of function concept has a significant effect on students' achievement goal motivation. [ABSTRACT FROM AUTHOR]

The problem of two equal collinear cracks weakening a poled transversely isotropic piezo-electro-magnetic plate is addressed under semi-permeable electro-magnetic boundary conditions on the crack faces. The problem is formulated employing Stroh formalism and solved using a complex variable technique. Closed form analytical expressions are derived for various fracture parameters. An illustrative numerical case study is presented for poledBaTiO3−CoFe2O4ceramic cracked plate to study the effect of prescribed electric load, magnetic load, and inter-crack distance on fracture parameters. Moreover, a comparative study is done of volume fraction, impermeable, and semi-permeable boundary conditions on fracture parameters. [ABSTRACT FROM PUBLISHER]

We study two new general integral operators for certain analytic functions in the unit disc U and give some sufficient conditions for these integral operators on some subclasses of analytic functions. [ABSTRACT FROM AUTHOR]

We study the extremal Dubinin problem in the geometric theory of functions of complex variables connected with the estimation of a functional defined on a system of nonoverlapping domains. A particular solution of this problem is obtained. [ABSTRACT FROM AUTHOR]

Some classes of metric spaces satisfying properties stronger than completeness but weaker than compactness have been studied by many authors over the years. One such significant family consists of those metric spaces on which every real-valued continuous function is uniformly continuous, which are widely known as Atsuji spaces or UC spaces. Recently in 2014, two new kinds of complete metric spaces are introduced, namely Bourbaki-complete and cofinally Bourbaki-complete metric spaces, whose idea has come from some new classes of sequences acting as generalizations of Cauchy sequences. Our major goal is to give several new equivalent conditions for metric spaces whose completions are one of the aforesaid spaces, especially in terms of some functions, sequences and geometric functionals. [ABSTRACT FROM AUTHOR]

This paper uses the convolution theorem of the Laplace transform to derive an inverse Laplace transform for the product of two parabolic cylinder functions in which the orders as well as the arguments differ. This result subsequently is used to obtain an integral representation for the product of two parabolic cylinder functions. The integrand in the latter representation contains the Gaussian hypergeometric function or alternatively can be expressed in terms of the associated Legendre function of the first kind. [ABSTRACT FROM PUBLISHER]

In this paper, we study the class of harmonic K-quasiconformal mappings of the unit disk U with finite Euclidean areas ∣f(U)∣euc. We first give the Schwarz-pick lemma (cf. [8]) for this class of mappings as follows: ∣fz(z)∣ ≤ √∣f(U)∣euc π(1 - k2) 1 -∣z∣, z ∊ U; where k = K-1/ K+1. Furthermore, we obtain the sharp coefficient estimates of this class of mappings. As an application, for harmonic mappings f ∊ S0H with finite ∣f(U)∣euc we obtain sharp coefficient estimates. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the isometric equivalence problem for the weighted composition operator Wu;φand the composi- tion operator Cφon the Hardy and the Dirichlet space. We show what properties the operators must satisfy to insure that they are isometric equivalent. [ABSTRACT FROM AUTHOR]

In this article the Srivastava-Owa-Ruscheweyh fractional derivative operator L αα λ is applied for defining and studying some new subclasses of analytic functions in the unit disk E: Inclusion results, radius problem and other results related to Bernardi integral operator are also discussed. Some applications related to conic domains are given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to find sufficient argument properties, such that the images of some subclasses of functions by the Libera transform have bounded arguments. [ABSTRACT FROM AUTHOR]

The object of the present investigation is to solve Fekete-Szegö problem for a new class Vλp (a, c, A,B) of p-valent analytic functions involving the Saitoh operator in the unit disk. We also obtain subordination results and some interesting corollaries for functions in Ap involving this operator. Relevant connections of the results obtained here with those given by earlier workers on the subject are also mentioned. [ABSTRACT FROM AUTHOR]

In this paper we introduce a kind of complex summation-integral type operators and study the approximation properties of these operators. We obtain a Voronovskaja-type result with quantitative estimate for these operators attached to analytic functions on compact disks. We also study the exact order of approximation. More important, our results show the overconvergence phenomenon for these complex operators. [ABSTRACT FROM AUTHOR]

In 1975, Richard O'Malley proved that every approximately con- tinuous function has approximate extrema, and this result provides an immediate solution to Scottish Book Problem 157. The purpose of this paper is to provide an additional proof of O'Malley's result. [ABSTRACT FROM AUTHOR]

For 0 ≼ µ ≼ λ; 0 ≼ α < 1; -π/2 < β < π/2 and m ε N U {0}, a new class Rm(λ, µ, α, β) of analytic functions defined by means of the differential operator Dmλµ is introduced. Basic properties of the class Rm(λ, µ, α, β) are investigated. Connections with previous known results are also pointed out. [ABSTRACT FROM AUTHOR]

By making use of a generalized integral operator, we introduce and investigate two new subclasses of p-valent analytic functions. Apart from deriving coefficient bounds and distortion inequalities for each of these function classes, we obtain several inclusion relations associated with the (n, δ)-neighborhoods of subclasses of p-valent analytic functions and their derivatives, which is defined by means of a certain general family of non-homogenous Cauchy-Euler differential equations. [ABSTRACT FROM AUTHOR]

For small ε > 0 , the system x ˙ = ε , z ˙ = h ( x , z , ε ) z , with h ( x , 0 , 0 ) < 0 for x < 0 and h ( x , 0 , 0 ) > 0 for x > 0 , admits solutions that approach the x -axis while x < 0 and are repelled from it when x > 0 . The limiting attraction and repulsion points are given by the well-known entry–exit function. For h ( x , z , ε ) z replaced by h ( x , z , ε ) z 2 , we explain this phenomenon using geometric singular perturbation theory. We also show that the linear case can be reduced to the quadratic case, and we discuss the smoothness of the return map to the line z = z 0 , z 0 > 0 , in the limit ε → 0 . [ABSTRACT FROM AUTHOR]

We study the uniqueness question of transcendental entire functions sharing one finite nonzero value with their derivatives in some angular domains instead of the whole complex plane. The results in the present paper improve and extend the corresponding results from Chang-Fang [2] and extend Theorem 3 from Zheng [15]. An example is provided to show that the results in this paper, in a sense, are best possible [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate some characterization for generalized Bessel functions of first kind to be in the new subclasses G(λ, α) and K(λ, α) of analytic functions. [ABSTRACT FROM AUTHOR]

Quasi-subordination is an underlying concept in the area of complex function theory. It is an interesting topic that unifies the concept of both subordination and majorization. There has been no work in this area for the past three decades except possibly a recent article (Haji Mohd and Darus, Fekete–Szegö problems for quasi-subordination classes, Abstr. Appl. Anal. 2012 (2012) 192956, 14 p.) [8] . Exploiting this article, we provide an estimate with k -th root transform for certain classes of analytic univalent functions using quasi-subordination. The authors sincerely hope that this article will revive this concept and encourage other researchers to work in this quasi-subordination in the near-future in the area of complex function theory. [ABSTRACT FROM AUTHOR]

We consider special Hilbert spaces of analytic functions of many infinite variables and examine composition operators on these spaces. In particular, we prove that under some conditions a translation operator is bounded and hypercyclic. [ABSTRACT FROM AUTHOR]

We study the singular points of analytic functions defined by Laplace-Stieltjes transformations which converge on the right half plane, by introducing the concept of X-order functions. We also confirm the existence of the finite X-order Borel points of such functions and obtained the extension of the finite X-order Borel point of two analytic functions defined by two Laplace-Stieltjes transformations convergent on the right half plane. The main results of this paper are improvement of some theorems given by Shang and Gao. [ABSTRACT FROM AUTHOR]

In Information Security, intrusion detection is the act of detecting actions that attempt to compromise the security goals. One of the primary challenges to intrusion detection is the problem of misjudgment, misdetection and lack of real time response to the attack. Various data mining techniques as clustering, classification and association rule discovery are being used for intrusion detection. The proposed hybrid technique combines data mining approaches like K Means clustering algorithm and RBF kernel function of Support Vector Machine as a classification module. The main purpose of proposed technique is to decrease the number of attributes associated with each data point. So, the proposed technique can perform better in terms of Detection Rate and Accuracy when applied to KDDCUP’99 Data Set. [ABSTRACT FROM AUTHOR]

Let k - ST[A, B], k ≥ 0, -1 ≤ B < A ≤ 1 be the class of normalized analytic functions defined in the open unit disk satisfying R((B-1)zf'(z)/f(z)-(A-1)/(B+1)zf'(z)/f(z)-(A+1)) > k/(B-1)zf'(z)/f(z)-(A-1)/(B+1)zf'(z)/f(z)-(A+1)-1/ and let k - UCV [A,B], k ≥ 0, -1 ≤ B < A ≤ 1 be the corresponding class satisfying R((B-1)zf'(z)/f(z)-(A-1)/(B+1)zf'(z)/f(z)-(A+1)) > k/(B-1)zf'(z)/f(z)-(A-1)/(B+1)zf'(z)/f(z)-(A+1)-1/. For an appropriate δ > 0, the δ neighborhood of a function f ∊ k -UCV[A, B] is shown to consist of functions in the class k - ST[A, B]. [ABSTRACT FROM AUTHOR]

In this paper we obtain an univalence criterion for analytic functions in the unit disk. [ABSTRACT FROM AUTHOR]

In the present paper we introduce a new subclass of analytic functions. We prove a sharp upper bound to the second Hankel determinant associated with the kth root transform [ f(zk) ]1/k of the normalized analytic function f(z), when it belongs to this class, using Toeplitz determinants. [ABSTRACT FROM AUTHOR]

Let A denote the family of all analytic functions f in the unit disk D with the normalization f ( 0 ) = 0 = f ′ ( 0 ) - 1 . In this note, we mainly consider the radius of univalence of F defined by F ( z ) = z 2 / f ( z ) , where f belongs to some subclasses of A or S , the class of univalent functions from A . The results of the present article sharpen the earlier known results. [ABSTRACT FROM AUTHOR]

The universality theoremasserts that the lower density of any set of shifts of the Riemann zeta-function which approximate a given analytic function with accuracy ɛ > 0 is strictly positive. It is proved that this set has strictly positive density for all but at most countably many ɛ > 0. [ABSTRACT FROM AUTHOR]

We discuss in detail the weak field limit of f(R, 풢) gravity taking into account analytic functions of the Ricci scalar R and the Gauss-Bonnet invariant 풢. Specifically, we develop, in metric formalism, the Newtonian, Post-Newtonian (PN) and Parametrized Post-Newtonian (PPN) limits starting from general f(R, 풢) Lagrangian. The special cases of f(R) and f(풢) gravities are considered. In the case of the Newtonian limit of f(R, 풢) gravity, a general solution in terms of Green's functions is achieved. [ABSTRACT FROM AUTHOR]

Let f : (ℝn, 0) → (ℝ, 0) be a nonconstant analytic function defined in a neighborhood of the origin 0 ∈ ℝn. The classical Łojasiewicz inequality states that there exist positive constants δ, c and l such that |f(x)| ≥ cd(x, f-1(0))l for |x| ≤ δ, where d(x, f-1(0)) denotes the distance from x to the set f-1(0). The Łojasiewicz exponent of f at the origin 0 ∈ ℝn, denoted by , is the infimum of the exponents l satisfying the Łojasiewicz inequality. In this paper, we establish a formula for computing the Łojasiewicz exponent of f in terms of the Newton polyhedron of f in the case where f is nonnegative and nondegenerate. [ABSTRACT FROM AUTHOR]

We prove several relations of the type ∣arg{zf''(z)/f'(z)}∣ ≤ ∣arg{f'(z)}∣ for functions satisfying some geometric conditions. [ABSTRACT FROM AUTHOR]

We continue the study of a Moutard-type transform for generalized analytic functions, which was initiated in [1]. In particular, we suggest an interpretation of generalized analytic functions as spinor fields and show that, in the framework of this approach, Moutard-type transforms for such functions commute with holomorphic changes of variables. [ABSTRACT FROM AUTHOR]