arXiv subjects

Saiful R Mondal

Publications and source records attributed to Saiful R Mondal.

8 recordsLinked to original sources

arXiv2025

On Lemniscate starlikeness of analytic functions and its application to special functions

This paper investigates the lemniscate starlikeness of analytic functions by deriving specific conditions on their power series coefficients. The study utilizes the Cauchy product of power series along with key inequalities involving the Pochhammer symbol and the Gamma function. The derived results are further applied to a number of special functions, providing parameter restrictions under which these functions become lemniscate starlike. The findings extend and refine several earlier results in this domain.

math.CV↗

arXiv2017

The Modified Lommel functions: monotonic pattern and inequalities

This article studies the monotonicity, log-convexity of the modified Lommel functions by using its power series and infinite product representation. Same properties for the ratio of the modified Lommel functions with the Lommel function, $\sinh$ and $\cosh$ are also discussed. As a consequence, some Turán type and reverse Turán type inequalities are given. A Rayleigh type function for the Lommel functions are derived and as an application, we obtain the Redheffer-type inequality.

math.CA↗

arXiv2017

Inequalities for the modified k-Bessel function

The article considers the generalized k-Bessel functions and represents it as Wright functions. Then we study the monotonicity properties of the ratio of two different orders k- Bessel functions, and the ratio of the k-Bessel and the m-Bessel functions. The log-convexity with respect to the order of the k-Bessel also given. An investigation regarding the monotonicity of the ratio of the k-Bessel and k-confluent hypergeometric functions are discussed.

math.CA↗

arXiv2016

Pathway fractional integral operators involving $\mathtt{k}$-Struve function

A new generalization called $\mathtt{k}$-Struve function and its properties given by Nisar and saiful very recently. In this paper, we establish the pathway fractional integral representation of $\mathtt{k}$-Struve function. Many special cases also established to obtain the pathway integral representation of classical Struve function.

math.CA↗

arXiv2016

Inequalities of extended Beta and extended hypergeometric functions

This paper studies the log-convexity of the extended beta functions. As a consequence, Turán-type inequalities are established.The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta functions,. The particular cases of those results also gives the Turán-type inequalities for extended confluent and extended Gaussian hypergeometric functions. Some reverse of Turán-type inequalities also derived.

math.CA↗

arXiv2016

Representation Formulae and Monotonicity of the Generalized k-Bessel Functions

This paper introduces and studies a generalization of the $\mathtt{k}$-Bessel function of order $ν$ given by \[\mathtt{W}^{\mathtt{k}}_{ν, c}(x):= \sum_{r=0}^\infty \frac{(-c)^r}{Γ_{\mathtt{k}}\left( r \mathtt{k} +ν+\mathtt{k}\right) r!} \left(\frac{x}{2}\right)^{2r+\fracν{\mathtt{k}}}. \] Representation formulae are derived for $\mathtt{W}^{\mathtt{k}}_{ν, c}.$ Further the function $\mathtt{W}^{\mathtt{k}}_{ν, c}$ is shown to be a solution of a second order differential equation. Monotonicity and log-convexity properties for the generalized $\mathtt{k}$-Bessel function $\mathtt{W}^{\mathtt{k}}_{ν, c}$ are investigated, particularly in the case $c=-1$. Several inequalities, including the Turán-type inequality are established.

math.CA↗

arXiv2016

On the geometric properties of the Bessel-Struve kernel function

This paper introduce the Bessel-Struve kernel functions $\mathcal{B}_ν$ defined on the unit disk in the complex plane. We studies the close-to-convexity of $\mathcal{B}_ν$ with respect to several starlike functions. Sufficient condition on $ν$ for which the function $z\mathcal{B}_ν$ is starlike is given.

math.CV↗

arXiv2016

One some differential subordination involving the Bessel-Struve kernel function

In this article we study the inclusion properties of the Bessel-Struve kernel functions in the Janowski class. In particular, we find the conditions for which the Bessel-Struve kernel functions maps the unit disk to right half plane. An open problem in this aspect are also given. The third order differential subordination involving the Bessel-Struve kernel is also considered. The results are derived by defining suitable classes of admissible functions. One of the recurrence relation of the Bessel-Struve kernel play an important role to derive the main results.

math.CV↗