Jugal Kishore Prajapat

• M. Sc. in Mathematics, Ph. D.
• Professor at Central University of Rajasthan

Generalized Laguerre polynomials have extensively been studied in various branches of applied mathematics and theoretical physics. It has however remained unexplored in the realms of Geometric Function Theory. Our aim in the present paper is to study and investigate the basic characteristics of the normalized form of this class of polynomials. Amon...

The Bessel function and its various generalizations have extensively been studied in various branches of applied mathematics and theoretical physics, including the Geometric Function Theory. In this paper, we study basic characteristics of Bessel functions of order µ and degree ν. Among the results that we investigate are the results giving the cha...

In this article, we study harmonic mappings f=h+g¯ in open unit disk with starlike functions as analytic part and obtain certain sharp results for injectivity, close-to-convexity, radius of fully starlike and radius of fully convex.

For $\alpha > -1$ and $\beta >0, $ let $\mathcal{B}_{\mathcal{H}}^0(\alpha, \beta)$ denote the class of sense preserving harmonic mappings $f=h+\overline{g}$ in the open unit disk $\mathbb{D}$ satisfying $|zh''(z)+\alpha(h'(z)-1)|\leq \beta-|zg''(z)+\alpha g'(z)|.$ First, we establish that each function belonging to this class is close-to-convex in...

In this paper, we study non sense-preserving harmonic mappings $f=h+\overline{g}$ in $\mathbb{D}$ when its analytic part $h$ is convex and injective in $\mathbb{D}$ and obtain radius of injectivety.

In this article, we consider a class of sense-preserving harmonic mappings whose analytic part is convex in one direction. We prove that functions in this class are close-to-convex for certain values of parameters. Further, we obtain bounds on pre-Schwarzian derivatives and bounds on the Bloch’s constant. Finally, we obtain coefficient bounds, grow...

In this article, we investigate the upper bounds on the coefficients for inverse of functions belongs to certain classes of univalent functions and in particular for the functions convex in one direction. Bounds on the Fekete-Szego functional and third order Hankel determinant for these classes have also investigated.

In this paper, we introduce a new class of sense preserving harmonic mappings [Formula: see text] in the open unit disk and prove that functions in this class are close-to-convex. We give some basic properties such as coefficient bounds, growth estimates, convolution and determine the radius of convexity for the sections of functions belonging to t...

In this paper, we study a family of sense-preserving harmonic mappings whose analytic part is convex in one direction. We first establish the bounds on the pre-Schwarzian norm. Next, we obtain radius of fully starlike and radius of fully convex for this family of harmonic mappings.

In this article, we determine conditions on the parameters of a generalized convolution operator such that it belongs to the Hardy space and to the space of bounded analytic functions. Results obtained are new and their usefulness is depicted by deducing several interesting examples.

In this article, we introduce a new family of sense preserving harmonic mappings f in the open unit disk and prove that functions in this family are close-to-convex. We give some basic properties such as coefficient bounds, growth estimates, convolution and determine the radius of convexity for the functions belonging to this family. In addition, w...

The aim of the paper is a study of a family of sense-preserving complex valued harmonic functions f that are normalized in the open unit disk, and such that its analytic part is convex in one direction. We prove the univalence and establish estimates on pre-Schwarzian derivative and the Bloch constant for co-analytic part of harmonic mapping. The b...

For the normalized analytic function $f$ in the open unit disk $\mathbb{D}:=\{z\in\mathbb{C}: |z|<1\}$, we consider the class $\mathcal{F}(\alpha)$ of functions $f$ satisfying the analytic characterization $\Re\left(1+\frac{zf''(z)}{f'(z)}\right) > -\frac{\alpha}{2\alpha -3}$, where $\alpha$ is an arbitrary number and is not less than $3/2$. For a...

In the present work, Mittag-Leffler functions with its normalization are considered. Several results are obtained so that these functions have certain geometric properties including starlikeness, convexity, close-to-convexity of order $\alpha$, and radius of starlikeness of order $\alpha$. Furthermore, we obtain certain condition so that the normal...

We introduce and investigate several new classes of analytic functions involving Srivastava-Attiya operator, and derive various useful properties and characteristics of these function classes by using the techniques of differential subordination. Several results are presented exhibiting relevant connections to some of the results proved here and th...

In this paper, the estimate for the third Hankel determinant H3;1(f) of Taylor coefficients of function, belonging to certain classes of analytic functions in the open unit disk D, are investigated.

In this paper, we show that every section of function in a family of convex function in one direction in the open unit disk are convex in \({\mathbb {D}}_{1{/}2}=\{z\in {\mathbb {C}}: |z|<1{/}2\}\). The radius 1/2 is best possible.

Differential subordination and superordination results associated with a generalized Hurwitz-Lerch Zeta function in the open unit disk are obtained by investigating appropriate classes of admissible functions. In particular some inequalities for generalized Hurwitz-Lerch Zeta function are obtained.

An operator associated with the Wright function is introduced in the open unit disk. Differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. In particular, some inequalities for modified Bessel functions are also obtained

In the present paper, we investigate certain geometric properties and inequalities for Wright function and mention few important consequences of our main results. A non-linear differential equation involving Wright function is also investigated.

This article provides a continuation of paper by Libera and Zlotkiewicz [Proc. Amer. Math. Soc. 87(2) (1983), 251-257], in which they investigated upper bounds on initial coefficients of inverse of a function defi�ned by integration of Caratheodory functions. We obtain upper bounds on Fekete-Szego functional and third Hankel determinant of such fun...

In this paper, some significant scientific errors in the paper by J.K. Prajapat entitled ‘Certain geometric properties of the Wright function’ are corrected.

In the present paper, we investigate upper bounds on the third Hankel determinants for the starlike and convex functions with respect to symmetric points in the open unit disk.

In this paper, we have obtained upper bound on third Hankel determinant for the functions belonging to the class of close-to-convex functions.

In the present investigation, the Mittag-Leffler functions with their normalization are considered. Several sufficient conditions are obtained so that the Mittag-Leffler functions have certain geometric properties including univalency, starlikeness, convexity and close-to-convexity in the open unit disk. Partial sums of Mittag-Leffler functions are...

The estimate of third Hankel determinant of the analytic function f(z) are investigated. The corrected version of a known results [2, Theorem 3.1 and Theorem 3.3] are also obtained

The estimate of third Hankel determinant (formula presented) of the analytic function f (z) = z + a2Z2 + a3Z2 + • • •, for which R(1+zf“(z)/f‘(z))>−1/2 are investigated. The corrected version of a known results [2, Theorem 3.1 and Theorem 3.3] are also obtained.

An integral operator for meromorphic multivalent function in the punctured unit disk is introduced by means of Hurwitz–Lerch Zeta function. Strong differential subordination and superordination results associated with the operator are obtained by investigating appropriate classes of admissible functions.

In this work, the Wright function with their normalizations are considered. Several conditions are obtained so that the Wright function has certain geometric properties including univalency, starlikeness, convexity and close-to-convexity in the open unit disk. Results obtained are new and their usefulness are depicted by deducing several interestin...

In this work, we introduce and investigate two new subclass of analytic and close-to-convex functions in the open unit disk U. For each of these function classes, several coefficient inequalities are established. The usefulness of the main results are depicted by showing improvement in earlier results. 2000 Mathematics Subject Classification: 30C45...

In this paper, we give a set of suffi�cient conditions for the univalence, starlikeness and convexity of a certain newly-defined general family of integral operators in the open unit disk. Relevant connections of the results presented here with those that were obtained in earlier works as well as several interesting corollaries and consequences of...

We first define a generalized form of a Hurwitz-Lerch zeta type function and then use it in constructing certain classes of analytic functions in the unit disk. In our investigation, we obtain various results for the classes introduced, thereby, exhibiting their useful properties and characteristics by adopting the techniques of differential subord...

This note gives the correct form of a result (Theorem 2, p. 478) published recently in [Math. Slovaca 60 (2010), 471–484].

In the present paper we derive various useful properties and characteristics for certain class of analytic functions by using the techniques of differential subordination. Some interesting corollaries and applications of the results presented here are also discussed.

In the present paper we derive various useful properties and characteristics for certain class of analytic functions by using the techniques of differential subordination. Some interesting corollaries and applications of the results presented here are also discussed.

This paper investigates various new subordination results for certain $p$-valent analytic functions involving a generalized multiplier transformation operator $J_{p}^{m}(\lambda ,l),m\in \mathbb{Z},$ defined recently by J.K. Prajapat [Math. Comput. Modelling, 55 (2012), 1456-1465]. Several lines of approach are followed to obtain the subordination...

Abstract. In the present paper we derive various useful properties and characteristics for certain class of meromorphic multivalent function involving a linear operator in the punctured unit disk U∗ = {z : z ∈ C and 0 < |z| < 1}, and derive various useful properties and characteristics of this function class. Several results are presented exhibitin...

The authors obtain subordination and superordination preserving properties for the new defined generalized operator involving the Srivastava-Attiya integral operator. Differential sandwich-type theorems for these univalent functions, and some consequences involving well-known special functions are also presented.

We obtain subordination and superordination preserving properties for a new generalized multiplier transformation operator, defined for multivalent functions in the open unit disk. A differential sandwich-type theorem for these multivalent functions, and some consequences are also presented.

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

A multiplier transformation is used to define certain new subclasses of analytic func-tions in the open unit disk U . For each of these new function classes, several inclusion rela-tionships are established. Some interesting corollaries and consequences of the main inclusion relationships are also considered.

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.

In this paper, we obtain some sufficient conditions for class of analytic functions involving fractional differintegral operator.

In this paper, we obtain some sufficient conditions for class of analytic functions involving fractional differintegral operator.

This paper presents a result relating to subordination of analytic function in the unit disk and provides an improved version of a result published recently in [Math. Slovaca 60 (4) (2010), 471-484]. Besides stating and proving here a corrected form of this result, we also consider its generalization. The concluding remarks indicate briefly other p...

The familiar Sǎlǎgean operator is used here to define a new subclass of analytic and univalent functions in the open unit disk U. In this note we obtain some sufficient conditions for functions belonging to this class and mention few important consequences of our main results.

We apply a fractional differintegral operator to a class of analytic functions and derive certain new sufficient conditions for the starlikeness of the functions in this class. The usefulness of the main results are depicted by deducing several interesting corollaries, and relations to some of the earlier results are also pointed out.

Making use of the familiar convolution structure of analytic functions, we introduce a general class of multivalently analytic functions and derive various useful properties and characteristics of this function class by using the techniques of differential subordination. Several other results are presented exhibiting relevant connections to some of...

By adapting a familiar convolution structure of analytic functions, we define and investigate in this paper certain new classes of analytic functions. Among the various results studied (by using the methods of differential subordinations) are some of the useful properties and characteristics attributed to these function classes. Several consequence...

In this paper we apply a fractional differintegral operator to a class of analytic functions and derive certain new sufficient conditions for the starlikeness of this class of functions. The usefulness of the main results are depicted by deducing several interesting corollaries and relevances with some of the earlier results are also pointed out.

In this paper we consider a class of analytic and multivalent functions to investigate some sufficient conditions for this class. Some interesting consequences of the main result are also mentioned.

In the present paper we investigate a class of multivalently analytic functions which essentially involves a Hadamard product of two multivalent functions. We apply the techniques of differential subordination and derive some useful characteristics of this function class. The applications to generalized hypergeometric functions and various conseque...

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.

Appealing to the familiar convolution structure of analytic functions, we introduce a general class of multivalently analytic functions, and derive several properties and characteristics of this function class by applying the differential subordination techniques. Relevant connections of the results stated here with those obtained in earlier works...

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.

Presented by V. Kiryakova We introduce and investigate a new class of multivalently analytic functions defined by means of a convolution structure. Important relationships of this class with other recently studied classes are specifically pointed out. Among the results investigated for this class are the coefficient estimates, growth and distortion...

In this paper we establish some generalized double inequalities involving the q-gamma function.

In this paper a general class of analytic functions involving a convolution structure is introduced. Among the results investigated are the various results depicting useful properties and characteristics of this function class by employing the techniques of differential subordination. Relevances of the main results with some known results are also...

The purpose of the present article is to investigate several new subclasses of analytic functions defined by using the Dziok-Srivastava operator, and to investigate various inclusion relationships for these subclasses. Some interesting corollaries and consequences of the results presented here are also discussed.

A known fractional calculus operator is used to define some new subclasses of analytic functions in the unit open disc U. For each of these new function classes, several inclusion relationships associated with (q,δ)-neighborhoods are established.

A known fractional calculus operator is used to define a new subclasses of analytic functions in the open unit disc. For each of these function classes some inclusion relationships associated with (q,δ)-neighborhoods are established.

We use the familiar convolution structure of analytic functions to introduce two new subclasses of multivalently analytic functions of complex order, and prove several inclusion relationships associated with the -neighborhoods for these subclasses. Some interesting consequences of these results are also pointed out.

We use the familiar convolution structure of analytic functions to introduce new class of analytic functions of complex order. The results investigated in the present paper include, the characterization and subordination properties for this class of analytic functions. Several interesting consequences of our results are also pointed out.

Some double inequalities involving the Euler’s gamma functions are obtained with the help of Psi function’s series representation.

A known family of fractional integral operators (with the Gauss hypergeometric function in the kernel) is used here 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 rela-tionships associated with the fractional in...

Making use of the familiar convolution structure of analytic functions, in this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order. Among the various results obtained here for each of these function classes, we derive the coefficient bounds and coefficient inequalities, and inclusion and neigh...

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 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.

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.

In the present paper we investigate a class of multivalently analytic functions which essentially involves a Hadamard product of two multivalent functions. We apply the techniques of differential subordination and derive some useful characteristics of this function class. The applications to generalized hypergeometric functions and various conseque...