Kottakkaran Sooppy Nisar

Operators constructed by means of q-Lagrange polynomials and A-statistical approximation

In this paper we construct some positive linear operators by means of q-Lagrange polynomials and prove some approximation results via A-statistical convergence. We also define and study the rate of A-statistical approximation of these operators by using the notion of modulus of continuity and Lipschitz class.

Marichev-Saigo-Maeda Fractional Integration Operators Involving Generalized Bessel Functions

Two integral operators involving Appells functions, or Horns function in the kernel are considered. Composition of such functions with generalized Bessel functions of the first kind is expressed in terms of generalized Wright function and generalized hypergeometric series. Many special cases, including cosine and sine function, are also discussed.

An efficient implicit regularized Lagrangian twin support vector regression

Twin support vector regression (TSVR) and Lagrangian TSVR (LTSVR) satisfy only empirical risk minimization principle. Moreover, the matrices in their formulations are always positive semi-definite. To overcome these problems, we propose an efficient implicit Lagrangian formulation for the dual regularized twin support vector regression, called IRLTSVR for short. By introducing a regularization term to each objective function, the optimization problems in our IRLTSVR are positive definite and implement the structural risk minimization principle. Moreover, the 1-norm of the vector of slack variable is replaced with 2-norm to make the objective functions strongly convex. Our IRLTSVR solves two systems of linear equations instead of solving two quadratic programming problems (QPPs) in TSVR and one large QPP in SVR, which makes the learning speed of IRLTSVR faster than TSVR and SVR. Particularly, we compare three implementations of IRLTSVR with existing approaches. Computational results on several synthetic and real-world benchmark datasets clearly indicate the effectiveness and applicability of the IRLTSVR in comparison to SVR, TSVR and LTSVR.

Fractional calculus and application of generalized Struve function

A new generalization of Struve function called generalized Galué type Struve function (GTSF) is defined and the integral operators involving Appell’s functions, or Horn’s function in the kernel is applied on it. The obtained results are expressed in terms of the Fox–Wright function. As an application of newly defined generalized GTSF, we aim at presenting solutions of certain general families of fractional kinetic equations associated with the Galué type generalization of Struve function. The generality of the GTSF will help to find several familiar and novel fractional kinetic equations. The obtained results are general in nature and it is useful to investigate many problems in applied mathematical science.

Differential subordinations and superordinations for generalized bessel functions

Differential subordination and superordination preserving properties for univalent functions in the open unit disk with an operator involving generalized Bessel functions are derived. Some particular cases involving trigonometric functions of our main results are also pointed out.

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.

Some Umbral Calculus Presentations of the Chan-Chyan-Srivastava Polynomials and the Erkuș-Srivastava Polynomials

In their recent investigation involving differential operators for the generalized Lagrange polynomials, Chan et. al. [3] encountered and proved a certain summation identity and several other results for the Lagrange polynomials in several variables, which are popularly known in the literature as the Chan-Chyan-Srivastava polynomials. These multivariable polynomials have been studied systematically and extensively in the literature ever since then (see, for example, [1], [4], [9], [11], [12] and [13]). In the present paper, we investigate umbral calculus presentations ofthe Chan-Chyan-Srivastava polynomials and also of their substantially more general form, the Erkus-Srivastava polynomials [9]. Some other closely-related results are also considered.

Numerical Method for Constructing Fixed Right Shift (FRS) Code for SAC-OCDMA Systems

In optical code division multiple access (OCDMA) systems, multiple access interference (MAI) problem which amplifies with the number of users actively involving in the network robustly bound the performance of such network. In this paper an algorithm to generate binary code sequences based on spectral amplitude coding (SAC) technique for CDMA under optical communication systems environment named fixed right shifting (FRS) is proposed. This algorithm is built with minimum cross correlation (MCC) using some type of Jordan matrices with straightforward algebraic methods. By using the code weight W and the number of users N, various sets of binary code sequences for the possibilities of even and odd combination are constructed. Furthermore, this algorithm allows users with different code sequences to transmit data with minimum likelihood of interference. Simulation results show our technique for an agreeable bit error rate (BER) of 10-12 can support a higher number of users in deterministic and stochastic methods compared to reported techniques such Modified Quadratic Congruence (MQC) and Modified Frequency Hopping (MFH).

Composition Formulas of Bessel-Struve Kernel Function

The generalized operators of fractional integration involving Appells function

Modeling and identification of heat exchanger process using least squares support vector machines

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