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H. M. Srivastava

Publications and source records attributed to H. M. Srivastava.

18 recordsLinked to original sources
arXiv2025

Convergence analysis of max-product and max-min Durrmeyer-type exponential sampling operators in Mellin Orlicz space

In the present study, we establish both pointwise and uniform convergence in the space of logarithmically uniformly continuous and bounded functions for the max-product and max-min Durrmeyer-type exponential sampling operators. Furthermore, the modular convergence of these operators is demonstrated within the framework of Orlicz space. In addition to the theoretical results, we provide numerical and graphical analyses for various kernel pairs, illustrating the convergence rates and approximation behavior of the proposed operators.

math.FA↗
arXiv2019

Fekete-Szego inequality for Classes of Starlike and Convex Functions

In the present paper, the new generalized classes of (p,q)-starlike and $(p,q)$-convex functions are introduced by using the (p,q)-derivative operator. Also, the (p,q)-Bernardi integral operator for analytic function is defined in an open unit disc. Our aim for these classes is to investigate the Fekete-Szego inequalities. Moreover, Some special cases of the established results are discussed. Further, certain applications of the main results are obtained by applying the (p,q)-Bernardi integral operator

math.GM↗
arXiv2019

Differential equation and recurrence relations of the Sheffer-Appell polynomial sequence: A matrix approach

Motivated by the effective impact of the Pascal functional and the Wronskian matrices, we investigate several identities and differential equation for the Sheffer-Appell polynomial sequence by using matrix algebra. The matrix approach, which we have used in this article, is convenient to derive the generating functions of the Sheffer-Appell polynomial sequence. By means of examples, we apply and also illustrate our results to an extended class of polynomial sequences.

math.CA↗
arXiv2019

A note on the value distribution of Differential Polynomials

Let $f$ be a transcendental meromorphic function, defined in the complex plane $\mathbb{C}$. In this paper, we give a quantitative estimations of the characteristic function $T(r,f)$ in terms of the counting function of a homogeneous differential polynomial generated by $f$. Our result improves and generalizes some recent results.

math.CV↗
arXiv2018

Third order differential subordination and superordination results for analytic functions involving the Srivastava-Attiya operator

In this article, by making use of the linear operator introduced and studied by Srivastava and Attiya \cite{srivastava1}, suitable classes of admissible functions are investigated and the dual properties of the third-order differential subordinations are presented. As a consequence, various sandwich-type theorems are established for a class of univalent analytic functions involving the celebrated Srivastava-Attiya transform. Relevant connections of the new results are pointed out.

math.CV↗
arXiv2018

Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions

We consider an integral transform introduced by Prabhakar, involving generalised multi-parameter Mittag-Leffler functions, which can be used to introduce and investigate several different models of fractional calculus. We derive a new series expression for this transform, in terms of classical Riemann-Liouville fractional integrals, and use it to obtain or verify series formulae in various specific cases corresponding to different fractional-calculus models. We demonstrate the power of our result by applying the series formula to derive analogues of the product and chain rules in more general fractional contexts. We also discuss how the Prabhakar model can be used to explore the idea of fractional iteration in connection with semigroup properties.

math.CA↗
arXiv2018

Potentials for a multidimensional elliptic equation with one line of degeneration and their applications to boundary value problems

Potentials play an important role in solving boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one singular coefficient. In the study of potentials, the properties of the fundamental solutions of the given equation are essentially used. At the present time, fundamental solutions of a multidimensional elliptic equation with one degeneration line are already known. In this paper, we investigate the potentials of the double- and simple-layers for this equation, with the help of which limit theorems are proved and integral equations containing in the kernel the density of the above potentials are derived.

math.AP↗
arXiv2017

A Novel Subclass of Univalent Functions Involving Operators of Fractional Calculus

In this paper, we introduce and investigate a novel class of analytic and univalent functions of negative coefficients in the open unit disk. For this function class, we obtain characterization and distortion theorems as well as the radii of close-to-convexity, starlikeness and convexity by using fractional calculus techniques.

math.CV↗
arXiv2015

A Novel Subclass of Analytic Functions Specified by a Family of Fractional Derivatives in the Complex Domain

In this paper, by making use of a certain family of fractional derivative operators in the complex domain, we introduce and investigate a new subclass $\mathcal{P}_{τ,μ}(k,δ,γ)$ of analytic and univalent functions in the open unit disk $\mathbb{U}$. In particular, for functions in the class $\mathcal{P}_{τ,μ}(k,δ,γ)$, we derive sufficient coefficient inequalities, distortion theorems involving the above-mentioned fractional derivative operators, and the radii of starlikeness and convexity. In addition, some applications of functions in the class $\mathcal{P}_{τ,μ}(k,δ,γ)$ are also pointed out.

math.CV↗
arXiv2015

The Clausenian hypergeometric function $_3F_2$ with unit argument and negative integral parameter differences

New explicit as well as manifestly symmetric three-term summationformulas are derived for the Clausenian hypergeometric series $_3F_2(1)$ with negative integral parameter differences. Our results generalize and naturally extend several similar relations published, in recent years, by many authors. An appropriate and useful connection is established with the quite underestimated 1974 paper by P. W. Karlsson.

math.CA↗
arXiv2013

Some New Symmetric Identities for the q-Zeta Type Functions

The main object of this paper is to obtain several symmetric properties of the q-Zeta type functions. As applications of these properties, we give some new interesting identities for the modified q-Genocchi polynomials. Finally, our applications are shown to lead to a number of interesting results which we state in the present paper.

math.NT↗
arXiv2013

Starlikeness problems for certain analytic functions concerned with subordinations

Let A_n be the class of functions f(z) which are analytic in the open unit disk U} with f(0)=0, f'(0)=1, f"(0)=f"'(0)=...=f^{(n)}=0 and f^{(n+1)}\neq0. Applying the results due to S. S. Miller (J. Math. Anal. Appl. 65(1978), 289-305), some interesting starlikeness problems concerned with subordinations are discussed. The results in the paper are extensions of results by M. Obradović (Hokkaido Math. J. 27(1998), 329-335).

math.CV↗
arXiv2013

Sufficient conditions for strongly Carathéodory functions

Applying the subordination principle for analytic functions in the open unit disk U, I. H. Kim and N. E. Cho (Comput. Math. Appl. 59(2010), 2067-2073) considered some sufficient conditions for Carathéodory functions. The purpose of this paper is to discuss some sufficient conditions for the class of strongly Carathéodory functions in U.

math.CV↗
arXiv2012

Double-Layer Potentials for a Generalized Bi-Axially Symmetric Helmholtz Equation

The double-layer potential plays an important r$\hat{\rm o}$le in solving boundary value problems of elliptic equations. Here, in this paper, we aim at introducing and investigating double layer potentials for a generalized bi-axially symmetric Helmholtz equation. By using some properties of one of Appell's hypergeometric functions in two variables, we prove limiting theorems and derive integral equations concerning a denseness of double-layer potentials.

math.AP↗
arXiv2001

Analytic continuation of the generalized hypergeometric series near unit argument with emphasis on the zero-balanced series

Various methods to obtain the analytic continuation near $z=1$ of the hypergeometric series $_{p+1}F_p(z)$ are reviewed together with some of the results. One approach is to establish a recurrence relation with respect to $p$ and then, after its repeated use, to resort to the well-known properties of the Gaussian hypergeometric series. Another approach is based on the properties of the underlying generalized hypergeometric differential equation: For the coefficients in the power series expansion around $z=1$ a general formula, valid for any $p$, is found in terms of a limit of a terminating Saalschützian hypergeometric series of unit argument. Final results may then be obtained for each particular $p$ after application of an appropriate transformation formula of the Saalschützian hypergeometric series. The behaviour at unit argument of zero-balanced hypergeometric series, which have received particular attention in recent years, is discussed in more detail. The related problem involving the behaviour of partial sums of such series is addressed briefly.

math.CA↗