Saiful R. Mondal

The Umbral operator and the integration involving generalized Bessel-type functions

Abstract The main purpose of this paper is to introduce a class of new integrals involving generalized Bessel functions and generalized Struve functions by using operational method and umbral formalization of Ramanujan master theorem. Their connections with trigonometric functions with several distinct complex arguments are also presented.

Inequalities of extended beta and extended hypergeometric functions

We study the log-convexity of the extended beta functions. As a consequence, we establish Turán-type inequalities. 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 give the Turán-type inequalities for extended confluent and extended Gaussian hypergeometric functions. Some reverses of Turán-type inequalities are also derived.

Composition Formulas of Bessel-Struve Kernel Function

The generalized operators of fractional integration involving Appells function

Coefficient Conditions for Starlikeness of Nonnegative Order

F_{3}(.)

Certain inequalities involving the k-Struve function

due to Marichev-Saigo-Maeda, is applied to the Bessel Struve kernel function

Inclusion of the Generalized Bessel Functions in the Janowski Class

S_{\alpha }\left( \lambda z\right),\lambda ,z\in \mathbb{C}

Zero-free approximants to derivatives of prestarlike functions

to obtain the results in terms of generalized Wright functions.The pathway integral representations Bessel Struve kernel function and its relation between many other functions also derived in this study.

Generalized fractional kinetic equations involving generalized Struve function of the first kind

� ∞ k 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.

On the positivity of certain trigonometric sums and their applications

We aim to introduce a k-Struve function and investigate its various properties, including mainly certain inequalities associated with this function. One of the inequalities given here is pointed out to be related to the so-called classical Turán-type inequality. We also present a differential equation, several recurrence relations, and integral representations for this k-Struve function.

On the Janowski convexity and starlikeness of the confluent hypergeometric function

Sufficient conditions on