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In this paper, we delve into the b -family of equations and explore regularity properties of its global solutions. Our findings reveal that, irrespective of the real choice of the constitutive parameter, when the initial datum is confined to an analytic Gevrey function the resulting global solution is analytic in both temporal and spatial variables. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce and investigate an interesting subclass of analytic and bi-univalent functions in the open unit disk . For functions belonging to the class , we obtain estimates on the first two Taylor–Maclaurin coefficients and . The results presented in this paper would generalize and improve some recent work of Srivastava et al. [H.M. Srivastava, A.K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010) 1188–1192]. [Copyright &y& Elsevier]

Abstract: For functions belonging to the class and , of analytic functions in , which are investigated in this paper, the author derives several interesting strong differential subordination results. These strong differential subordinations are established by means of a special case of the extended multiplier transformations namely where , and , A number of interesting consequences of some of these strong subordination results are discussed. Relevant connections of some of the new results obtained in this paper with those in earlier works are also provided. [Copyright &y& Elsevier]

Abstract: In a recent paper [M. Masjed-Jamei, H.M. Srivastava, An integral expansion for analytic functions based upon the remainder values of the Taylor series expansions, Appl. Math. Lett. 22 (2009) 406–411], a new type of integral expansions for analytic functions was introduced and investigated. In this sequel to our earlier paper, we make use of the aforementioned expansion in order to explicitly obtain the general solutions of the following functional equation: for various kinds of real sequences and , where (as usual) is the th derivative of the unknown function at . We also present some illustrative examples in this sense. [Copyright &y& Elsevier]

The paper investigates large-time behaviour of positive solutions to a generalized Dickman equation. The asymptotic behaviour of dominant and subdominant positive solutions is analysed and a structure formula describing behaviour of all solutions is proved. A criterion is also given for sufficient conditions on initial functions to generate positive solutions with prescribed asymptotic behaviour with values of their weighted limits computed. [ABSTRACT FROM AUTHOR]

In the literature adaptive Fourier decomposition is abbreviated as AFD that addresses adaptive rational approximation, or alternatively adaptive Takenaka–Malmquist system approximation. The AFD type approximations may be characterized as adaptive approximations by linear combinations of parameterized Szegö and higher order Szegö kernels. This note proposes two kinds of such analytic approximations of which one is called maximal-energy AFDs, including core AFD, Unwending AFD and Cyclic AFD; and the other is again linear combinations of Szegö kernels but generated through SVM methods. The proposed methods are based on the fact that the imaginary part of an analytic signal is the Hilbert transform of its real part. As consequence, when a sequence of rational analytic functions approximates an analytic signal, then the real parts and imaginary parts of the functions in the sequence approximate, respectively, the original real-valued signals and its Hilbert transform. The two approximations have the same errors in the energy sense due to the fact that Hilbert transformation is a unitary operator in the L 2 space. This paper for the first time promotes the complex analytic method for computing Hilbert transforms. Experiments show that such computational methods are as effective as the commonly used one based on FFT. [ABSTRACT FROM AUTHOR]

In this paper we revisit Hamilton’s normalized Ricci flow, which was thoroughly studied via a PDE approach in Kavallaris and Suzuki (2010). Here we provide an improved convergence result compared to the one presented Kavallaris and Suzuki (2010) for the critical case λ = 8 π . We actually prove that the convergence towards the stationary normalized Ricci flow is realized through any time sequence. [ABSTRACT FROM AUTHOR]

In this paper, a class of second order dissipative system (1) x ̈ ( t ) + a ( t ) x ̇ ( t ) + ∇ f ( x ( t ) ) = 0 is studied, where f : R N → R is analytic and non-convex, a : R + → R + is continuous and nonincreasing with lim t → ∞ a ( t ) = 0 . We give a sufficient condition for the convergence of global and bounded solutions of (1). The condition shows that the rate of convergence of damping coefficient a ( t ) is related to the Lojasiewicz exponent of the analytic function f . [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present formulas betwixt Legender and Chebyshev expansion coefficients for a piecewise smooth (or Dini–Lipschitz) function, analyze the error bounds for the Piessens’ algorithm and present a new algorithm with operations for computation of the first coefficients of the Legendre expansion. Finally, we show the identity to the formulas given by Iserles [5] for analytic functions in a neighborhood of . [Copyright &y& Elsevier]

Abstract: In this paper, we obtain extensions of sufficient conditions for analytic functions in the open unit disk to be starlike and convex of order . Our results unify and extend some starlikeness and convexity conditions for analytic functions discussed by Mocanu (1988) , Uyanik et al. (2011) and others. [Copyright &y& Elsevier]

Abstract: This paper studies the inventory model for deteriorating items with trapezoidal type demand rate. We adopt the rigorous methods of mathematics to develop the analytic solution procedures to remove shortcomings of those of Cheng and Wang (2009) . [Copyright &y& Elsevier]

Abstract: In this paper, we consider certain subclasses of analytic functions with bounded radius and bounded boundary rotation and study the mapping properties of these classes under an integral operator. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the weak–strong uniqueness of the Cauchy problem for the 2D dissipative quasi-geostrophic equation. We proved the weak–strong uniqueness when one of the two weak solutions lies in the regular class . [Copyright &y& Elsevier]

Abstract: The main purpose of the present paper is to derive some results for analytic functions whose takes values on concave domains. As special cases of these results, several new sufficient conditions for univalency and starlikeness of analytic functions are obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we obtain new sufficient conditions for the operator to be univalent in the open unit disc , where each of the functions satisfy the condition . [Copyright &y& Elsevier]

Abstract: For analytic functions and in the open unit disk , a new integral operator is introduced. The main object of this paper is to obtain a univalence condition and the order of convexity for the integral operator . [Copyright &y& Elsevier]

Abstract: In the present paper, we introduce and investigate a certain subclass of meromorphic close-to-convex functions. Such results as coefficient inequalities, convolution property, distortion property and radius of meromorphic convexity are derived. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new general integral operator defined by the Hadamard product. Furthermore, we obtained new sufficient conditions for this operator to be univalent in the open unit disk. [Copyright &y& Elsevier]

Abstract: In this paper, we give a set of sufficient conditions for the normalized form of the generalized Bessel function to be univalent in the open unit disk, and further we obtain certain inequalities containing normalized Bessel functions. [Copyright &y& Elsevier]

Abstract: The purpose of the present paper is to introduce two subclasses of -valent Bazilevic functions by using the generalized operator and to investigate various properties for these subclasses. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce two new subclasses of the function class of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients and for functions in these new subclasses. [Copyright &y& Elsevier]

Abstract: In this paper we obtain some applications of first order differential subordination and superordination results involving generalized Sălăgean integral operator for certain normalized analytic functions. Some of our results generalize previously known results. [Copyright &y& Elsevier]

Abstract: In this paper, the order of simultaneous approximation and Voronovskaja-type theorems with quantitative estimate for complex Bernstein–Durrmeyer-type polynomials attached to analytic functions on compact disks are obtained. Our results show that extension of the complex Bernstein–Durrmeyer-type polynomials from real intervals to compact disks in the complex plane extends approximation properties. [Copyright &y& Elsevier]

Abstract: The harmonic function in the open unit disc can be written as a sum of an analytic and an anti-analytic function, , where and are analytic functions in , and are called the analytic part and co-analytic part of , respectively. One of the most important questions in the study of the classes of such functions is related to bounds on the modulus of functions (growth) or modulus of the derivative (distortion), because the growth theorem and distortion theorem give the compactness of the classes of these functions. In this paper we consider both of these questions with the shear construction method. [Copyright &y& Elsevier]

Abstract: In this paper, we find the necessary and sufficient conditions for functions in the generalized class of uniformly starlike and uniformly convex functions of order and also consequences of the results are pointed out. [Copyright &y& Elsevier]

Abstract: A normalized analytic function defined on the open unit disk is a Janowski starlike function if is subordinated to , where and are complex numbers satisfying the conditions and . In this paper, a new class of analytic functions defined by means of subordination is introduced. Sufficient conditions are obtained for functions in this class to be Janowski starlike. The results obtained extend earlier known works. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the complex Gauss–Weierstrass integral operators defined on a space of analytic functions in two variables on the Cartesian product of two unit disks. Then, we study the geometric properties and statistical approximation process of our operators. [Copyright &y& Elsevier]

Abstract: We denote by , the class of all analytic functions in the unit disc with the normalization . For a positive number , we denote by the class of all , such that , and satisfying the condition A function is said to be in if . In this paper, we find conditions on , and such that is included in the class of all starlike functions of order , or the class of all strongly starlike functions of order , or , respectively. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, we investigate the majorization properties for certain classes of multivalent analytic functions defined by the Sălăgean operator. Moreover, we point out some new and interesting consequences of our main result. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, we introduce and investigate two interesting subclasses of normalized analytic and univalent functions in the open unit disk whose inverse has univalently analytic continuation to . Among other results, bounds for the Taylor–Maclaurin coefficients and are found in our investigation. [Copyright &y& Elsevier]

Abstract: In the present paper we investigate the majorization properties for certain classes of multivalent analytic functions defined by multiplier transformation. Moreover, we point out some new or known consequences of our main result. [Copyright &y& Elsevier]

Abstract: In this paper we derive some criteria for univalence of a general integral operator for analytic functions in the open unit disk. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce new subclasses of analytic and univalent functions and establish certain results concerning the quasi-Hadamard product of functions in these subclasses. Our result includes several previous known results as special cases. [Copyright &y& Elsevier]

Abstract: Here we investigate a majorization problem involving starlike function of complex order belonging to a certain class defined by means of fractional derivatives. Relevant connections of the main results obtained in this paper with those given by earlier workers on the subject are also pointed out. [Copyright &y& Elsevier]

Abstract: In this paper we derive several subordination results for a certain class of analytic functions defined by the Salagean operator. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the higher order linear differential equation on an angle. We apply Nevanlinna sectorial theory to estimate the growth of solutions of the equation restricted in the angle and prove the existence of asymptotic value of the derivative of solutions of the equation in the angle. By using these results we can improve some known results in the plane. [Copyright &y& Elsevier]

Abstract: Let be a fixed analytic and univalent function of the form and be the subclass consisting of analytic and univalent functions which satisfy the inequality . In this paper, we study the ratio of a function of the form to its sequence of partial sums of the form where the coefficients of satisfy the above condition. Also, we determine sharp lower bounds for , , and . [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the structure of the discrete spectrum of the system of non-selfadjoint difference equations of first order using the uniqueness theorems of analytic functions. We also obtained the sufficient conditions on coefficients of this system under which its discrete spectrum is finite. [Copyright &y& Elsevier]

Abstract: An interesting criterion was given by Ponnusamy and Singh [S. Ponnusamy, V. Singh, Convolution properties of some classes of analytic functions, Internal Report, SPIC Science Foundation, 1990.] for convolution properties of functions in the class . In this paper we shall get a new criterion for convolution properties of functions in this class. [Copyright &y& Elsevier]