S.P. Goyal

• University of Rajasthan

In this paper, we introduce and investigate some inclusion theorems, convolution theorems and class preserving transforms for subclasses of the meromorphic multivalent function associated with the El-Ashwah operator. Some interesting corollaries and consequences of the main results are pointed out.

In the present paper, we obtain the estimates on initial coefficients of normalized analytic function f in the open unit disk with f and its inverse g = f

In 2005, Ponnusamy and Sahoo have introduced a special subclass of univalent functions Un(λ) (n ∈ N, λ > 0) and obtained some geometrical properties, including strongly starlikeness and convexity, for the functions of this subclass Un(λ). Moreover, they have studied some important properties of an integral transform connected with these subclasses....

In the present paper certain subclasses of close-to-convex functions are investigated. In particular, we obtain an estimate for the Fekete-Szegő functional for functions belonging to our class, coefficient estimates and a sufficient condition. The results presented here would provide extensions of those given in some earlier works.

In this paper we introduce and investigate a certain subclass of functions which are analytic in the punctured unit disk and meromorphically close-to-convex. The sub-ordination property, inclusion relationship, coefficient inequalities, distortion theorem and a sufficient condition for our subclass of functions are derived. The results presented he...

The purpose of the present paper is to consider some sufficient conditions for analytic functions in the open unit disk to be starlike. Here we establish three theorems by using Jack’s lemma and a simple result contained in Lemma 2.2. Our theorems provide improvements of the results about sufficient conditions for starlike functions given earlier by...

In this paper we investigate the majorization problem for a subclass of p-valently analytic functions involving the Wright generalized hypergeometric function. Some useful consequences of the main result are mentioned and relevance with some of the earlier results are also pointed out.

The aim of this paper is to introduce two new classes of analytic function by using principle of subordination and the Dziok- Srivastava operator. We further investigate convolution properties for these calsses. We also �nd necessary and su�cient condition and coe�- cient estimate for them.

In this paper, we obtain extensions of sufficient conditions for analytic functions f(z)f(z) in the open unit disk UU to be starlike and convex of order αα. Our results unify and extend some starlikeness and convexity conditions for analytic functions discussed by Mocanu (1988) [4], Uyanik et al. (2011) [3] and others.

Estimates for second and third Maclaurin coefficients of certain bi-univalent functions in the open unit disk defined by convolution are determined. Certain special cases are also indicated.

In the present paper we obtain some conditions on a, b and c to verify that zp 2F1(a; b; c; z) to be in various subclasses of starlike and convex functions. we also examine an integral operator related to the p-valent hypergeometric function.

The aim of the present paper is to obtain sufficient conditions for starlike functions of order $\beta$. We establish two theorems. The first theorem provides improvement of the sufficient conditions for starlikeness obtained earlier by several research workers such as Lewandowski et al. [5], Li and Owa [6], Nunokawa et al. [8,9], Ramesha et al. [1...

In the present paper, we investigate differential inequalities for certain analytic functions using a differential operator in the open unit disk. Our findings extend several results recently obtained by M. Nunokawa et al. [Comput. Math. Appl. 56, No. 11, 2908–2914 (2008; Zbl 1165.30333)].

We investigate a majorization problem involving starlike meromorphic functions of complex order belonging to a certain subclass of meromorphic univalent functions defined by an integral operator introduced recently by A. Y. Lashin [Comput. Math. Appl. 59, No. 1, 524–531 (2010; Zbl 1189.30025)].

In the present investigation, sharp upper bounds of |ηa 2 2 -a 3 | for functions f(z)=z+a 2 z 2 +a 3 z 3 +⋯ belonging to certain subclasses of uniformly starlike functions with respect to symmetric points are obtained. Also, certain applications of the main results to certain subclasses defined by convolution are considered. In addition, Fekete-Sze...

The main object of this paper is to derive several subordination results for a class of analytic functions defined by a new generalized differential operator.

The purpose of this paper is to derive subordination and superordination results involving Dziok-Srivastava operator for a family of analytic multivalent functions in the open unit disk. These results are applied to obtain sandwich results. Some results which are useful in geometric function theory are also obtained as special cases of the results...

The purpose of this paper is to derive subordination and superordination results involving Dziok-Srivastava operator for a family of analytic multivalent functions in the open unit disk. These results are applied to obtain sandwich results. Some results which are useful in geometric function theory are also obtained as special cases of the results...

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.

We investigate familar geometric properties of the classes S p * [A,B], K p [A,B] and S p μ [A,B]. Also, results obtained earlier are derived as special cases from our main results.

We establish certain results concerning the quasi-Hadamard product for classes related to meromorphic p-valent analytic functions with positive coefficients.

In the present paper, we investigate majorization properties for the subclass of analytic functions defined by an extension, introduced by Saitoh, of the well-known Carlson-Shaffer linear operator, using differential subordination. Relevant connections of the main results obtained in this paper with those given by earlier workers are also pointed o...

The purpose of the present article is to establish two theorems for a class of analytic univalent functions defined in the open unit disk. The results are proved by using techniques involving the principle of differential subordination. Connections of these theorems with Bazilevic˘ functions are considered and the main results are applied to obtain...

Srivastava-Attiya operator is used to define some new subclasses of strongly starlike and strongly convex functions of order β and type α in the open unit disk U . For each of these new function classes, several inclusion relationships are established. Some interesting corollaries and applications of the results presented here are also discussed.

In the present paper, sharp upper bounds of |a 3 − µa 2 2 | for the functions f (z) = z + a 2 z 2 + a 3 z 3 + ... belonging to a new subclass of Sakaguchi type functions are obtained. Also, application of our results for subclass of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szegö inequalit...

The purpose of the present paper is to investigate some argument properties for certain analytic functions in the open unit disk associated with the convolution structure. Some interesting applications are also considered as special cases of main results presented here.

Making use of certain extended derivative operator of Ruscheweyh type, we introduce a new class J p (λ, µ, α) of meromorphic multivalent function in the punctured disk D = {z : z ∈ C, 0 < |z| < 1}, and obtain some sufficient conditions for the functions belonging to this class.

We derive certain new argument properties of a class of multivalent analytic functions defined in the open unit disk by using a theorem recently established by A. Y. Lashin [JIPAM, J. Inequal. Pure Appl. Math. 5, No. 4, Paper No. 111, 5 p., electronic only (2004; Zbl 1086.30018)]. Certain interesting (known or new) results are derived in the form o...

We derive subordination and superordination results for a family of normalized analytic functions in the open unit disk defined by integral operators. We apply this to obtain sandwich results and generalizations of some known results.

Making use of the familiar convolution structure and subordination of analytic functions, in this paper we introduce and investigate two new subclasses of meromorphic multivalent functions. Some results con-cerning partial sums of certain meromorphic multivalent functions are established.

The object of the present paper is to discuss the coefficient estimates for multivalent functions belonging to the starlike and convex classes. Further, by using the Dziok-Srivastava linear operator, several distortion inequalities for these classes are also established.

Making use of a certain generalized linear operator, we introduce some new classes of analytic p-valent functions in the open unit disk U. Several inclusion relations and the (n,δ)-neighborhood of functions belonging to these classes are obtained. Some interesting consequences of these results are also pointed out.

We obtain some sufficient conditions for an analytic and p-valent function f(z) defined on the unit disc, to be starlike of order α.

The aim of the present paper is to establish some integral mean inequalities for the generalized fractional calculus operators of analytic multivalent functions. Appropriate integral mean inequalities for the class of starlike and convex analytic multivalent functions are also discussed. Our results provide generalizations and unifications of some...

In the present paper, we introduce and study some new subclasses of analytic functions (which are multivalent, starlike, and convex) defined by certain integral operators. We shall establish inclusion relations for these classes, and derive some properties of our integral operators of functions in these subclasses.

In this paper we deal with the Cauchy problem for the space time fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with Riemann-Liouville derivative of order α∈(0,1]. The finite Hankel, finite sine and Laplace transforms are used to solve the problem and the solution i...

The aim of this paper is to extend the domain of the Hurwitz zeta function from the set of complex numbers to the set of bicomplex numbers and to discuss zeros and analytic continuation of this function.

The aim of this paper is to define bicomplex gamma and beta functions. We also discuss conditions of validity and T-holomorphicity for these functions. Various properties including a Legendre duplication formula, a Gauss multiplication theorem and a binomial theorem are established. These functions, which are believed to be new, will provide a fund...

The aim of this paper is to obtain integral mean inequalities for the generalized fractional derivatives of order + (0 < 1,0 n) of functions belonging to certain general subclass of analytic multivalent functions. Some properties of this general subclass of functions are also proved. Our results generalize various integral mean inequalities obtaine...

Here, a new class of p-valent analytic functions is defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator. The coefficient bounds, extreme points, integral representations, distortion bounds, radius of starlikeness and convexity and neighbourhood results are obtained for this class. Our r...

In this paper we establish a very general and useful theorem which interconnects the Laplace transform and the generalized Weyl fractional integral operator involving the multivariable H-function of related functions of several variables. Our main theorem involves a multidimensional series with essentially arbitrary sequence of complex numbers. By...

We define a new class of functions which are analytic and p-valent with negative coefficients, by using fractional differ-integral operators studied recently by the authors. Characterization, distortion theorems and other interesting properties of this class of functions are studied. Some special cases of main results are also pointed out.

We establish a general theorem exhibiting a relationship existing between the Laplace transform and the generalized Weyl fractional integral operator (FIO) of related functions. This theorem is very general in nature and involves a multidimensional series with essentially arbitrary sequence of complex numbers. By suitably assigning different values...

M. Saigo and H. J. Glaeske [Math. Nachr. 147, 285–306 (1990; Zbl 0737.46030)] have investigated operators of fractional calculus involving Gauss hypergeometric functions (which generalize the classical operators of Riemann-Liouville and Weyl and also the Erdelyi-Kober operators) in weighted L p -spaces and space F p,μ introduced by Mc-Bride. In thi...

The present paper systematically investigates a new class of functions, which are analytic and p-valent with negative coefficients, involving a fractional differ-integral S 0,z μ,ν,η (-∞<μ<1). Characterization, inclusion and distortion theorems of this class of functions are obtained and some special cases of the main results are also given.

The main aim of this paper is to establish a theorem which asserts an interesting relationship between the multidimensional Laplace transform, the multidimensional Varma transform and the generalized Weyl fractional integral involving product of a general class of multivariable polynomials and a generalized polynomial set. By specializing the vario...

The object of the present paper is to calculate the single Dirichlet average (for several variables) of x t (t∈ℂ) which is a key formula to find Dirichlet averages of functions x n (n∈ℕ), e x and of a general class of polynomials. It is also aimed at setting some equivalence relations between the Riemann-Liouville fractional integral operator and t...

Recently, Srivastava, Pathan and Kamarujjama established several results for generalised Voigt functions which play an important role in several diverse fields of physics—such as astrophysical spectroscopy and the theory of neutron reactions. In the present paper we aim to generalise some partly bilateral and partly unilateral representations and g...

In the present work, we evaluate a unified Eulerian type integral whose integrand involves the product of a polynomial system and the multivariable H-function having general arguments. Our integral formula encompasses a very large number of integrals and provides interesting unifieation and extensions of several known (e.g., [1], [3], [4], [5], [9]...

The aim of the present paper is to establish two theorems connecting the Laplace transform and a certain class of generalized fractional integral operators involving a generalized polynom叫 set. These theorems provide .usful extension and unification of a number of (known or new) results for vaious classes of fractional integral operators. Several i...

In the present work, we introduce and study essentially a class of multi-dimensional modified fractional calculus operators involving a general class of polynomials in the kernel. These operators are considered in the space of functionsM γ (R + n ). Some mapping properties and fractional differential formulas are obtained. Also images of some e...

The aim of this paper is to derive a solution of a certain class of convolution integral equation of Fredholm type whose kernel involves a generalized polynomial set. Our main result is believed to be general and unified in nature. A number of (known or new) results follow as special cases, simply by specializing the coefficients and parameters inv...

The main object of this paper is to derive a fractional integral operator (involving a generalized polynomial set) of the product of a general class of multivariable polynomials and the H-function of several complex variables. On account of the general nature of the operator, the multivariable polynomials and the H-function of several complex varia...

First we evaluate an integral involving the product of general classes of polynomials, Konhauser biorthogonal polynomials and the multivariable H-function. This integral is then employed to establish an expansion formula for the product of a general class of polynomials and the multivariable H-function in a series of biorthogonal polynomials. The r...

This paper is a continuation of part I [ibid. 22, No. 5, 403-411 (1991; Zbl 0747.44002)]. In the present paper, it is shown how these operators can be identified with elements of the algebra of functions having the Mellin convolution as the product. Inversion formulas and the relations of our operators with the generalized Hankel transforms are als...

An attempt has been made to present a unified theory of the classical statistical distributions associated with the multivariate generalized Dirichlet distributions involving Fox’s H-function [see C. Fox, Trans. Am. Math. Soc. 98, 395-429 (1961; Zbl 0096.308)] with general arguments. In particular, mathematical expectations of a general class of po...

In the present paper the authors prove a theorem which asserts an interesting relationship between the classical Laplace transform, a certain class of Whittaker transforms, and a Weyl fractional integral involving a general class of polynomials with essentially arbitrary coefficients. By specializing the various parameters involved, this general th...

In the present paper the authors derive a number of interesting expressions for the composition of certain multidimensional fractional integral operators involving a general class of polynomials with essentially arbitrary coefficients. It is shown how these fractional integral operators can be identified with elements of the algebra of functions ha...

CERTAIN INEQUALITIES FOR THE KAMPÉ DE FÉRIET FUNCTION