Search

The paper proposes a new approach for function approximation by ‘estimating’ the second derivative, using Taylor series, where the samples of the function and its first derivatives at the sample points are known. Without such ‘estimation’, these initial data, can approximate the function traditionally using the first order Taylor approximation, but with more error. If we desire to improve the approximation via second order Taylor series, then we can estimate the ‘pseudo’ second derivatives of the function in three different ways. All these three ways are investigated in this paper. The pseudo second derivatives help in computing many more sample points of the function within each sampling interval. Thus, the approach acts like a mathematical ‘magnifying glass’. Two examples are treated to compare the efficiencies of the methods. Also, a qualitative study for upper bound of error of the approximations is studied in detail. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, the authors derive several sharp coefficient estimates for the function class consisting of the inverses of functions in a certain class of spirallike functions in the open unit disk , which was introduced by Libera. They also obtain a number of sharp coefficient bounds of functions in the more general classes and , each of which is introduced here. Some of the results derived in this paper would generalize those in a recent work of Kapoor and Mishra. [Copyright &y& Elsevier]

Abstract: For analytic functions the remainder term of quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points and a sum of semi-axes , for Gauss–Radau quadrature formula with Chebyshev weight function of the third kind. Starting from the explicit expression of the corresponding kernel, derived by Gautschi, we determine the locations on the ellipses where maximum modulus of the kernel is attained. The obtained values confirm the corresponding conjectured values given by Gautschi in his paper [W. Gautschi, On the remainder term for analytic functions of Gauss–Lobatto and Gauss–Radau quadratures, Rocky Mounatin J. Math. 21 (1991) 209-206]. In this way the last unproved conjecture from the mentioned paper is now verified. [Copyright &y& Elsevier]

Abstract: In a recent paper, Hernández and Salanova proposed an interesting Newton-like method for the solution of nonlinear Fredholm integral equations. The aim of the present paper is to carry over this method to nonlinear operator equations of similar type. By using a functional analytic approach, the presentation becomes much clearer and more general. Apart from this, some new results in the Banach space setting as well as in the applications are obtained. [Copyright &y& Elsevier]

Abstract: Results about the study of nonanalytic systems’ center-focus and bifurcations of limit cycles are hardly seen in published references up till now. In this paper, we investigated the problems of determining center or focus and bifurcations for a class of planar quasi cubic analytic systems. The recursive formula to figure out generalized focal values is given, ulteriorly the conditions for four limit cycles from the origin or the point at infinity are obtained and center problems are considered. What is worth pointing out is that we offer a kind of interesting phenomenon that the exponent parameter λ control the non-analyticity of studied system in this paper. In terms of nonanalytic differential systems, our work is new. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a subclass of analytic functions with complex order is introduced by means of a family of nonhomogenous Cauchy–Euler differential equations. The main object of the paper is to determine coefficient bounds for the class, and obtain the exact results. These results extend some known theorems. [Copyright &y& Elsevier]

Abstract: In this paper, the authors introduce and investigate the various properties of two subclasses and of multivalent analytic functions. In particular, some sufficient conditions for the subclass of analytic functions, argument properties, the growth theorems, distortion theorems and covering theorems are obtained. Some of the results, presented in this paper, would generalize and extend the corresponding results of earlier authors. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to investigate various properties and characteristics of the Dziok–Srivastava operator introduced in Dziok and Srivastava [J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999) 1–13]. Our paper is motivated essentially by the familiar work Liu and Srivastava [J.-L. Liu, H.M. Srivastava, Certain properties of the Dziok–Srivastava operator, Appl. Math. Comput. 159 (2004) 485–493] which has been recently published. [Copyright &y& Elsevier]

The main object of the present paper is to investigate several interesting properties and characteristics of a linear operator Hp,q,s(α1) which was recently introduced and studied in a series of papers by Dziok and Srivastava [Appl. Math. Comput. 103 (1999) 1–13; Adv. Stud. Contemp. Math. 5 (2002) 115–125; Integral Transform. Spec. Funct. 14 (2003) 7–18]. The various properties and characteristics of the linear operator Hp,q,s(α1), which are considered in this paper, are associated with (for example) the principle of differential subordination between analytic functions and a certain one-parameter family of integral operators. [Copyright &y& Elsevier]

In this paper is to investigate an majorization problem for the class Sp,qn(γ). Relevant connections of the main result obtained in this paper with those given by earlier workers on the subject are also pointed out. [Copyright &y& Elsevier]

Abstract: In this note, we show that the proof of Theorem 3.8 in the above paper is wrong since there exists several errors. Furthermore, we conjecture that the conclusion of Theorem 3.8 in the paper only holds true for the case . [Copyright &y& Elsevier]

Let A be the class of analytic functions f which are regular and satisfying the conditions f ( 0 ) = 0 , f ′ ( 0 ) = 1 . In other words each f in A has the power series representation f ( z ) = z + a 2 z 2 + a 3 z 3 + ⋯ in the open unit disc D = { z | | z | < 1 } . For every q ∈ (0, 1), let q -difference operator be defined as follows D q f ( z ) = f ( z ) − f ( q z ) z ( 1 − q ) ( z ∈ D ) Making use of the above operator we define a class of analytic functions, so called q -close-to-convex function with respect to Janowski starlike functions and the class of such functions is defined by K q ( A, B ). In the present paper we will study on this class. [ABSTRACT FROM AUTHOR]

Let D be the open unit disk in the complex plane C and H ( D ) the class of all analytic functions on D . Let φ be an analytic self-map of D and ψ ∈ H ( D ) . In this paper the boundedness and compactness of the generalized weighted composition operator D φ , ψ n f = ψ f ( n ) ∘ φ from the Zygmund space to the Bloch–Orlicz space and the little Bloch–Orlicz space are characterized. [ABSTRACT FROM AUTHOR]

In the paper we generalize the class of multivalent Mocanu functions. The main object is to obtain characterizations and inclusion properties for defined classes of functions. Some applications of the main results to classes defined by the Srivastava–Wright operator are also considered. [ABSTRACT FROM AUTHOR]

Let D be the open unit disk in the complex plane, φ an analytic self-map of D and ψ an analytic function on D . Let D n be the n th differentiation operator and W φ, ψ the weighted composition operator. In this paper the boundedness and compactness of the generalized product-type operators D n W φ, ψ and W φ, ψ D n from weighted Bergman–Orlicz spaces to Bloch–Orlicz spaces are characterized. [ABSTRACT FROM AUTHOR]

In the present paper we establish several fuzzy differential subordinations regarding the operator L α m , given by L α m : A → A , L α m f ( z ) = ( 1 − α ) R m f ( z ) + α S m f ( z ) , where R m f ( z ) denote the Ruscheweyh derivative, S m f ( z ) is the Sălăgean operator and A n = { f ∈ H ( U ) , f ( z ) = z + a n + 1 z n + 1 + ⋯ , z ∈ U } is the class of normalized analytic functions with A 1 = A . A certain fuzzy class, denoted by S L F m ( δ , α ) , of analytic functions in the open unit disk is introduced by means of this operator. By making use of the concept of fuzzy differential subordination we will derive various properties and characteristics of the class S L F m ( δ , α ) . Also, several fuzzy differential subordinations are established regarding the operator L α m . [ABSTRACT FROM AUTHOR]

For an analytic function φ : D → D , the composition operator C φ is the operator on the Hardy space H 2 defined by C φ f = f ○ φ for all f in H 2 . In this paper, we give necessary and sufficient conditions for the composition operator C φ to be binormal where the symbol φ is a linear fractional selfmap of D . Furthermore, we show that C φ is binormal if and only if it is centered when φ is an automorphism of D or φ( z ) = sz + t , | s | + | t | ≤ 1. We also characterize several properties of binormal composition operators with linear fractional symbols on H 2 . [ABSTRACT FROM AUTHOR]

In this sequel to the recent work (see Srivastava, 2015), we investigate some further properties of a linear operator associated with Srivastava’s λ -generalized Hurwitz–Lerch zeta function, which are related to a certain class of meromorphically univalent functions in the punctured unit disk defined here by means of the Hadamard product (or convolution). We also give several interesting corollaries and consequences of the main results presented in this paper. [ABSTRACT FROM AUTHOR]

Tabulation method is usually adopted to describe the mapping relation of the analytic function of the local rules of Cellular Automaton. Although tabulation method is quite suitable to describe the mapping relation among discrete variables, there are numerous if-else sentences for the state decision of independent variables in computer programming. In this paper, we define an analytic function of the local rules of an Elementary Cellular Automaton by constructing the recognition function of the states of the cell and the neighbors. Therefore, a huge number of calculations by if-else sentences are transferred to the function calculation due to the adoption of the function of the local rules during the evolution of the ECA. Finally, the simulation results show that the programming structure is optimized and the programming efficiency is enhanced. In addition, the proposed method can also be extended to other 2-state cellular automata. [ABSTRACT FROM AUTHOR]

This paper is concerned with the generalized nonlinear second-order equation and its discrete counterpart furnished with different lattices, respectively. By the unified symmetry analysis method, the complete group classifications of the equations are performed. In the sense of point symmetry, all of the vector fields of the continuous nonlinear equation are obtained. As its special cases, the vector fields of some other important nonlinear equations are provided. Then, we develop the unified group classification method for dealing with partial difference schemes (P Δ S), all of the point symmetries of the difference schemes are presented with respect to the given arbitrary analytic function f ( u ) . [ABSTRACT FROM AUTHOR]

Let H be a reproducing kernel Hilbert space of analytic functions on the unit disk D. The best kernel approximation problem for H is the following: given any positive integer n and any function f ∈ H find the best norm approximation of f by a linear combination of no more than n kernel functions K (z , z k) , 1 ≤ k ≤ n. The purpose of this paper is to prove the existence of best kernel approximation for weighted Bergman spaces with standard weights. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper we consider the problem of numerical analytic continuation for an analytic function on a strip domain . The key difference with the known methods is that a novel iteration regularization method with a priori and a posteriori parameter choice rule is presented. The comparison in numerical aspect with other methods is also discussed. [Copyright &y& Elsevier]

Abstract: The paper concerns the differential subordination with the expression combined by arithmetic and geometric means: where and α are real numbers such that , , . For , , we also study the differential subordination Several applications of the studied subordination in the theory of analytic functions are given. [Copyright &y& Elsevier]

Abstract: In the paper we introduce general classes of multivalent analytic functions defined by the subordination. In particular, we define the class of multivalent prestarlike functions. By using the Ruscheweyh’s duality theory we investigate convolution properties related to multivalent prestarlike functions and various inclusion relationships between defined classes of functions. Some applications involving well-known classes of functions defined by linear operators are also considered. [Copyright &y& Elsevier]

Abstract: This paper concerns the partial derivatives of the eigen-triplet of the quadratic matrix polynomial , where are complex analytic matrix valued functions, is a complex parameter vector. First, the analyticity theorem for simple eigenvalues and the corresponding eigenvectors is given. Second, a new method is proposed to compute partial derivatives of the eigen-triplet. The derivatives of the eigen-triplet can be obtained by solving algebraic linear equations of order , where it only requires the information of the eigen-triplet whose partial derivatives are to be computed, and what is more important, the condition numbers of the coefficient matrices are “better” than those of the nonsingular coefficient matrices arisen in the bordered matrix method [1] and Nelson’s method [5]. Numerical tests show the feasibility and efficiency of the new method. The results are better or at least comparable with current methods. [Copyright &y& Elsevier]

Abstract: Let denote the class of analytic functions in the unit disc on the complex plane . If the operator satisfiesfor all , then it is called subordination-preserving operator on the class . In this paper we present a new result of this form which generalize some of the earlier and is connected with the Wilf’s conjecture. The applications of main result are also presented. [Copyright &y& Elsevier]

Abstract: Let be the class of all analytic functions f in the open unit disk of the form . For and , two subclasses and of are introduced. In this paper, we find suitable conditions on , c and such that for each satisfying for all , the functionbelongs to or . Here denotes the usual class of starlike of order in . We also determine necessary conditions so that implies thatwhere will be specified. [Copyright &y& Elsevier]

Abstract: In the present paper, we obtain the subordination- and superordination-preserving properties of a certain general family of nonlinear integral operators which are defined on the space of normalized analytic functions in the open unit disk. The sandwich-type results for these integral operators are also presented. [Copyright &y& Elsevier]

Abstract: Motivated essentially by the recent works of Srivastava et al. , Frasin and Aouf , Xu et al. , and other authors, the authors of the present sequel investigate the coefficient estimate problems associated with an interesting general subclass of analytic and bi-univalent functions in the open unit disk , which is introduced here. In particular, for functions belonging to this general class , the problems involving the estimates on the first two Taylor–Maclaurin coefficients and are investigated. The results presented in this paper generalize and improve the aforecited recent works of Frasin and Aouf and Xu et al. (see also a closely-related earlier investigation by Srivastava et al. ). [Copyright &y& Elsevier]

Abstract: In this paper, we apply the collocation methods to a class of nonlinear convolution Volterra integral equations with multiple proportional delays (NCVIEMPDs). We shall present the existence, uniqueness and regularity properties of analytic solution for this type equation, and then analyze the convergence and superconvergence properties of the collocation solution. The numerical results verify our theoretical analysis. [Copyright &y& Elsevier]

Abstract: In this paper we present the generalized Adomian–Rach theorem and the generalized Rach–Adomian–Meyers modified decomposition method for solving multi-order nonlinear fractional ordinary differential equations. We consider different classes of initial value problems for nonlinear fractional ordinary differential equations, including the case of real-valued orders and another case of rational-valued orders, which are solved by the present method. This method can treat any analytic nonlinearity. The coefficients of the solution in the form of a generalized power series are determined by a convenient recurrence scheme, which does not involve integration operations compared with the classic Adomian decomposition method. [Copyright &y& Elsevier]

Abstract: In the present paper, we derive various properties and characteristics of the Srivastava–Khairnar–More integral operator. Such results as inclusion relationships, integral preserving properties, inequality properties, convolution properties, subordination and superordination properties, and sandwich-type results are obtained. Relevant connections of the results presented here with those obtained in earlier works are also pointed out. [Copyright &y& Elsevier]

Abstract: In this paper, analytically investigated is a generalized one-dimensional time-dependent Schrödinger equation. Using Darboux transformation operator technique, we construct the first-order Darboux transformation and the real-valued condition of transformed potential for the generalized Schrödinger equation. To prove the equivalence of the supersymmetry formalism and the Darboux transformation, we investigate the relationship among first-order Darboux transformation, supersymmetry and factorization of the corresponding effective mass Hamiltonian. Furthermore, the nth-order Darboux transformations are constructed by means of different method. Finally, by using Darboux transformation, some analytical solutions are generated in a recursive manner for some examples of the Schrödinger equation. [Copyright &y& Elsevier]

Abstract: When an analytic function is not univalent, it is often of interest to approximate it by univalent functions. In this paper we introduce a measure of the non-univalency of a function and we derive a method for constructing the best starlike univalent approximations of analytic functions with respect to it, suitable for both practical problems and numerical implementation. [Copyright &y& Elsevier]

Abstract: In this paper, by making use of the familiar concept of neighborhoods of p-valently analytic functions, we prove coefficient bounds, distortion inequalities and associated inclusion relations for the (n, δ)-neighborhoods of a family of p-valently analytic functions and their derivatives, which is defined by means of a certain general family of non-homogenous Cauchy–Euler differential equations. [Copyright &y& Elsevier]

Abstract: A Galerkin boundary element method based on interpolatory Hermite trigonometric wavelets is presented for solving 2-D potential problems defined inside or outside of a circular boundary in this paper. In this approach, an equivalent variational form of the corresponding boundary integral equation for the potential problem is used; the trigonometric wavelets are employed as trial and test functions of the variational formulation. The analytical formulae of the matrix entries indicate that most of the matrix entries are naturally zero without any truncation technique and the system matrix is a block diagonal matrix. Each block consists of four circular submatrices. Hence the memory spaces and computational complexity of the system matrix are linear scale. This approach could be easily coupled into domain decomposition method based on variational formulation. Finally, the error estimates of the approximation solutions are given and some test examples are presented. [Copyright &y& Elsevier]

Abstract: Let denote the space of all analytic functions on the open unit disk of . Let φ be an analytic self-map of and . In this paper, the boundedness and compactness of the generalized weighted composition operator from the F(p, q, s) space to the Bloch-type space and the little Bloch-type space are characterized. [Copyright &y& Elsevier]

Abstract: In this paper a simple method to obtain the analytical model of a flexible robot is presented, which turns out to be more efficient, from a computational point of view, than the classic assumed modes method. The presented method consists of using appropriate linear combinations of the modes of each link as basis functions to evaluate the deflection, in such a way as to minimize the dependency of the position of the generic link on the Lagrangian variables of the previous links. Hence, the number of terms of the inertia matrix and of the Coriolis and centrifugal vectors is significantly reduced. First, the model is derived, provided that the links are homogeneous and with constant cross-section, by analytically or otherwise by numerically calculating the parameters of the closed-form expression of the Lagrangian function of the generic link supposed free; afterwards, the analytical dynamic model of the whole robot is obtained by using an iterative interconnection algorithm, which can be easily implemented by using a symbolic manipulation language. The simplicity and efficiency of the proposed method is illustrated by considering the analytic expression of the kinetic energy of the end-effector in different cases and with significant comparison examples. [Copyright &y& Elsevier]

Abstract: In the present paper, we introduce and investigate a new subclass of analytic functions in the open unit disk , which is defined by the convolution (f μ )−1 ∗ f(z), whereSeveral interesting properties including (for example) integral-preserving properties of this analytic function class are also considered. [Copyright &y& Elsevier]

Abstract: In the present paper, we introduce and investigate classes of analytic functions involving the Srivastava–Attiya operator. Basic properties for β-uniformly starlike functions of order γ are studied, such as inclusion relations, sufficient conditions, coefficient inequalities and distortion inequalities. The results are also extended to β-uniformly convex, close-to-convex, and quasi-convex functions. Relevant connections of the results presented here with those obtained in earlier works are also pointed out. [Copyright &y& Elsevier]

Abstract: The object of the present paper is to obtain a more general condition for univalence of meromorphic functions in the . The significant relationships and relevance with other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results. [Copyright &y& Elsevier]

Abstract: In the present paper, by using the Srivastava–Attiya operator, we define two new subclasses of k-fold symmetric analytic functions. Some interesting properties of these subclasses such as integral representations, extreme points, close convex hulls and subordinations are obtained, which generalize and refine some previous results. [Copyright &y& Elsevier]

Abstract: Let A be the class of analytic functions in the open unit disk U. A function f in A satisfying the normalization is said to be in the class SP n if D n f is a parabolic starlike function, where D n is a notation of the Salagean operator. In this paper, several basic properties and characteristics of the class SP n are investigated. These include subordination, convolution properties, class-preserving integral operators, and Fekete-Szegö problems. [Copyright &y& Elsevier]

Abstract: The concept of analyticity for complex functions on time scale complex plane was introduced by Bohner and Guseinov in 2005. They developed completely delta differentiability, delta analytic functions on products of two time scales, and Cauchy–Riemann equations for delta case. In this research paper we study on continuous, discrete and semi-discrete analytic functions and developed completely nabla differentiability, nabla analytic functions on products of two time scales, and Cauchy–Riemann equations for nabla case. [Copyright &y& Elsevier]

Abstract: In the geometric function theory (GFT) much attention is paid to various linear integral operators mapping the class S of the univalent functions and its subclasses into themselves. In Hohlov obtained sufficient conditions that guarantee such mappings for the operator defined by means of Hadamard product with the Gauss hypergeometric function. In our earlier papers as , etc., we extended his method to the operators of the generalized fractional calculus (GFC, ). These operators have product functions of the forms m+1 F m and m+1 Ψ m and integral representations by means of the Meijer G- and Fox H-functions. Here we propose sufficient conditions that guarantee mapping of the univalent, respectively of the convex functions, into univalent functions in the case of the celebrated Dziok–Srivastava operator (:J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103, No 1 (1999), pp. 1–13) defined as a Hadamard product with an arbitrary generalized hypergeometric function p F q . Similar conditions are suggested also for its extension involving the Wright p Ψ q -function and called the Srivastava–Wright operator (Srivastava, ). Since the discussed operators include the above-mentioned GFC operators and many their particular cases (operators of the classical FC), from the results proposed here one can derive univalence criteria for many named operators in the GFT, as the operators of Hohlov, Carlson and Shaffer, Saigo, Libera, Bernardi, Erdélyi–Kober, etc., by giving particular values to the orders p ⩽ q +1 of the generalized hypergeometric functions and to their parameters. [Copyright &y& Elsevier]

Abstract: The main purpose of the present paper is to derive some new criteria for meromorphic multivalent starlike functions. [Copyright &y& Elsevier]

Abstract: In this paper, the order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for the complex genuine Durrmeyer polynomials attached to analytic functions on compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for the genuine Durrmeyer polynomials, namely the extensions of the approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we discuss the properties of the Schwarzian derivative, integral means and the affine and linear invariant families of biharmonic mappings. First, we introduce the Schwarzian derivative for biharmonic mappings F =∣z∣2 G + H, and obtain several necessary and sufficient conditions for to be analytic. Second, we introduce the subordination of biharmonic mappings and obtain inequalities for integral means of subordinate biharmonic mappings. Finally, we introduce the affine and linear invariant families of biharmonic mappings and prove several estimates related to the Jacobian of functions in these invariant families. [Copyright &y& Elsevier]

Abstract: For analytic functions normalized with and in the open unit disk , a new class of satisfying some conditions with some complex numbers and is introduced. The object of the present paper is to discuss some properties for of associated with close-to-convex and starlike of order in . [Copyright &y& Elsevier]

Abstract: Let denote the class of all analytic functions on the open unit disk of . Let be an analytic self-map of and . The weighted composition operator is defined byThe boundedness and compactness of weighted composition operators from area Nevanlinna spaces into Bloch spaces and little Bloch spaces are characterized in this paper. [Copyright &y& Elsevier]