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Motivated by the familiar q-hypergeometric functions, we introduce a new family of integral operators and obtain new sufficient conditions of univalence criteria. Several corollaries and consequences of the main results are also pointed out. [ABSTRACT FROM AUTHOR]

We will study a maximal solution of the time-space fractional heat equation in complex domain. The fractional time is taken in the sense of the Riemann-Liouville operator, while the fractional space is assumed in the Srivastava-Owa operator. Here we employ some properties of the univalent functions in the unit disk to determine the upper bound of this solution. The maximal solution is illustrated in terms of the generalized hypergeometric functions. [ABSTRACT FROM AUTHOR]

This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters. Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. Special attention is given to many equivalent inequalities and to conditions under which the constant factors involved in inequalities are the best possible. Many particular cases of Hilbert-type inequalities are presented with numerous applications. A large number of major books and recent research papers published during 2009-2012 are included to stimulate new interest in future study and research. [ABSTRACT FROM AUTHOR]

The aim of this research paper is to obtain explicit expressions of (1 - x)-2a 2F1[2b+ja,b ; -4x/(1x)2 ) for j = 0, ±1, ±2. For j = 0, we have the well-known transformation formula due to Gauss. The results are derived with the help of generalized Watson's theorem. Some known results obtained earlier follow special cases of our main findings. [ABSTRACT FROM AUTHOR]

Previous work on time-optimal satellite slewing maneuvers, with one satellite axis (sensor axis) required to obey multiple path constraints (exclusion from keep-out cones centered on high-intensity astronomical sources) reveals complex motions with no part of the trajectory touching the constraint boundaries (boundary points) or lying along a finite arc of the constraint boundary (boundary arcs). This paper examines four cases in which the sensor axis is either forced to follow a boundary arc, or has initial and final directions that lie on the constraint boundary. Numerical solutions, generated via a Legendre pseudospectral method, show that the forced boundary arcs are suboptimal. Precession created by the control torques, moving the sensor axis away from the constraint boundary, results in faster slewing maneuvers. A two-stage process is proposed for generating optimal solutions in less time, an important consideration for eventual onboard implementation. [ABSTRACT FROM AUTHOR]

The effect of tilted harmonic excitation and parametric damping on the chaotic dynamics in an asymmetric magnetic pendulum is investigated in this paper. The Melnikov method is used to derive a criterion for transition to nonperiodic motion in terms of the Gauss hypergeometric function. The regular and fractal shapes of the basin of attraction are used to validate theMelnikov predictions. In the absence of parametric damping, the results showthat an increase of the tilt angle of the excitation causes the lower bound for chaotic domain to increase and produces a singularity at the vertical position of the excitation. It is also shown that the presence of parametric damping without a periodic fluctuation can enhance or suppress chaos while a parametric damping with a periodic fluctuation can increase the region of regular motions significantly. [ABSTRACT FROM AUTHOR]

For zero-balanced Gaussian hypergeometric functions F(a,b;a + b;x), a, b > 0, we determine maximal regions of ab plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for each xε (0, 1). Thereby an exhausting answer is given to the open problem from the work by Anderson et al., 1990. [ABSTRACT FROM AUTHOR]

Sufficient conditions on a sequence {ak} of nonnegative numbers are obtained that ensures f(z) = ... akzk is starlike of nonnegative order in the unit disk. A result of Vietoris on trigonometric sums is extended in this pursuit. Conditions for close to convexity and convexity in the direction of the imaginary axis are also established. These results are applied to investigate the starlikeness of functions involving the Gaussian hypergeometric functions. [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]

We introduce and study a subclass ΣP (γ, k, λ, c) of meromorphic univalent functions defined by certain linear operator involving the generalized hypergeometric function. We obtain coefficient estimates, extreme points, growth and distortion inequalities, radii of meromorphic starlikeness, and convexity for the class ΣP (γ, k, λ, c) by fixing the second coefficient. Further, it is shown that the class ΣP (γ, k, λ) is closed under convex linear combination. [ABSTRACT FROM AUTHOR]

We investigate the Shintani functions attached to the spherical and nonspherical principal series representations of SL(3,R). We give the explicit formulas of the radial part of Shintani functions and evaluate the dimension of the space of Shintani functions. [ABSTRACT FROM AUTHOR]

The stress induced in a loaded beam will not exceed some threshold, but also its maximum deflection, as for all the elastic systems, will be controlled. Nevertheless, the linear beam theory fails to describe the large deflections; highly flexible linear elements, namely, rods, typically found in aerospace or oil applications, may experience large displacements-but small strains, for not leaving the field of linear elasticity-so that geometric nonlinearities become significant. In this article, we provide analytical solutions to large deflections problem of a straight, cantilevered rod under different coplanar loadings. Our researches are led by means of the elliptic integrals, but the main achievement concerns the Lauricella F D(3) hypergeometric functions use for solving elasticity problems. Each of our analytic solutions has been individually validated by comparison with other tools, so that it can be used in turn as a benchmark, that is, for testing other methods based on the finite elements approximation. [ABSTRACT FROM AUTHOR]

For p-valently Janowski starlike and convex functions defined by applying subordination for the generalized Janowski function, the sharp upper bounds of a functional ∣ap+2 - μa2 p+1∣ related to the Fekete-Szeg¨o problem are given. [ABSTRACT FROM AUTHOR]

Motivated by a multiplier transformation and some subclasses of meromorphic functions which were defined by means of the Hadamard product of the Cho-Kwon-Srivastava operator, we define here a similar transformation by means of the Ghanim and Darus operator. A class related to this transformation will be introduced and the properties will be discussed. [ABSTRACT FROM AUTHOR]

We have obtained a new summation formula for 2ψ2 bilateral basic hypergeometric series by the method of parameter augmentation and demonstrated its various uses leading to some development of etafunctions, q-gamma, and q-beta function identities. [ABSTRACT FROM AUTHOR]

To understand the tripological contact phenomena, both mathematical and experimental models are needed. In this work, fractal mathematical models are used to model the experimental results obtained from literature. Fractal geometry, using a deterministic Cantor structure, is used to model the surface topography, where recent advancements in thermoviscoelastic creep contact of rough surfaces are introduced. Various viscoelastic idealizations are used to model the surface materials, for example, Maxwell, Kelvin-Voigt, Standard Linear Solid and Jeffrey media. Such media are modelled as arrangements of elastic springs and viscous dashpots in parallel and/or in series. Asymptotic power laws, through hypergeometric series, were used to express the surface creep as a function of remote forces, body temperatures and time. The introduced models are valid only when the creep approach of the contact surfaces is in the order of the size of the surface roughness. The obtained results using such models, which admit closed-form solutions, are displayed graphically for selected values of the systems' parameters; the fractal surface roughness and various material properties. Results obtained showed good agreement with published experimental results, where the utilized methodology can be further extended to the utilization for the contact of surfaces within micro- and nano-electronic devices, circuits and systems. [ABSTRACT FROM AUTHOR]

By making use of the Dziok-Srivastava operator, we introduce a new class of meromorphically multivalent functions. Some inclusion properties of functions belonging to this class are derived. [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]

We investigate several results concerning the differential subordination of analytic andmultivalent functions which is defined by using a certain fractional derivative operator. Some special cases are also considered. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study the p-valent analytic functions in the unit disk and satisfy the differential subordinations z(Ip)r, λ(f(z))(j+1)/(p - j)(ɔp(r, λ)f(z))(j) < (a + (aB + (A- B)β)z)/a(1 + Bz), where ɔp(r, λ) is an operator defined by Sălăgean and β is a complex number. Further we define a new related integral operator and also study the Fekete-Szego problem by proving some interesting properties. [ABSTRACT FROM AUTHOR]

Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the class TSml(α, β, γ). In particular, we obtain integral means inequalities for the function f that belongs to the class TSml(α, β, γ) in the unit disc. [ABSTRACT FROM AUTHOR]

The author continues to study series transformations for the Euler-Mascheroni constant γ. Here, we discuss in detail recently published results of A. I. Aptekarev and T. Rivoal who found rational approximations to γ and γ + log q (q ∈ ℚ>0) defined by linear recurrence formulae. The main purpose of this paper is to adapt the concept of linear series transformations with integral coefficients such that rationals are given by explicit formulae which approximate γ and γ + log q. It is shown that for every q ∈ ℚ>0 and every integer d ≥ 42 there are infinitely many rationals am/bm for m = 1, 2, … such that ∣γ + log q - am/bm∣ ⪡ ((1 - 1/d)d/(d - 1)4d)m and bm ∣ Zm with log Zm ∼ 12d2m2 for m tending to infinity. [ABSTRACT FROM AUTHOR]

We investigate several distortion inequalities involving fractional calculus, Ruscheweyh derivatives, and some well-known integral operators. In special cases, the results presented in this paper provide new approaches to several previously known results. [ABSTRACT FROM AUTHOR]

We study several properties of matrix variate beta type 3 distribution. We also derive probability density functions of the product of two independent random matrices when one of them is beta type 3. These densities are expressed in terms of Appell's first hypergeometric function F1 and Humbert's confluent hypergeometric function Φ1 of matrix arguments. Further, a bimatrix variate generalization of the beta type 3 distribution is also defined and studied. [ABSTRACT FROM AUTHOR]

The authors define a new subclass of A of functions involving complex order in the open unit disk U. For this new class, we obtain certain inclusion properties involving the Gaussian hypergeometric functions. [ABSTRACT FROM AUTHOR]

A Markov chain with state space {0,…,N} and transition probabilities depending on the current state is studied. The chain can be considered as a discrete Ornstein-Uhlenbeck process. The probability that the process hits N before 0 is computed explicitly. Similarly, the probability that the process hits N before -M is computed in the case when the state space is {-M,…,0,…,N} and the transition probabilities pi,i+1 are not necessarily the same when i is positive and i is negative. [ABSTRACT FROM AUTHOR]

For λ > -1 and μ ≥ 0, we consider a liner operator Iλμ on the class A of analytic functions in the unit disk defined by the convolution (fμ)(-1)*f(z), where fμ = (1-μ)z2F1(a, b, c; z) + μz(z2F1(a, b, c; z))', and introduce a certain new subclass of A using this operator. Several interesting properties of these classes are obtained. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to give some characterizations for a (Gaussian) hypergeometric function to be in various subclasses of starlike and convex functions. We also consider an integral operator related to the hypergeometric function. [ABSTRACT FROM AUTHOR]