Physical Sciences and Mathematics Commons^™

Univalent Functions With Positivecoefficients Involving Touchard Polynomials, Gangadharan Murugusundraramoorthy, Saurabh Porwal

Al-Qadisiyah Journal of Pure Science

The purpose of the present paper is to establish connections between various subclasses of analytic univalent functions by applying certain convolution operator involving Touchard polynomials. To be more precise, we investigate such connections with the classes of analytic univalent functions with positive coefficients in the open unit disk $\mathbb{U}.$

Convex Analysis Of Minimal Time And Signed Minimal Time Functions, D. V. Cuong, B. S. Mordukhovich, Mau Nam Nguyen, M. L. Wells

Mathematics and Statistics Faculty Publications and Presentations

In this paper we first consider the class of minimal time functions in the general setting of locally convex topological vector (LCTV) spaces. The results obtained in this framework are based on a novel notion of closedness of target sets with respect to constant dynamics. Then we introduce and investigate a new class of signed minimal time functions, which are generalizations of the signed distance functions. Subdifferential formulas for the signed minimal time and distance functions are obtained under the convexity assumptions on the given data.

On Fejér Type Inequalities For Convex Mappings Utilizing Generalized Fractional Integrals, A. Kashuri, R. Liko

Applications and Applied Mathematics: An International Journal (AAM)

In this work, we first establish Hermite-Hadamard-Fejér type inequalities for convex function involving generalized fractional integrals with respect to another function which are generalization of some important fractional integrals such as the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. Moreover, we obtain some trapezoid type inequalities for these kind of generalized fractional integrals. The results given in this paper provide generalization of several inequalities obtained in earlier studies.

On Dc And Local Dc Functions, Liam Jemison

University Honors Theses

In this project we investigate the class of functions which can be represented by a difference of convex functions, hereafter referred to simply as 'DC' functions. DC functions are of interest in optimization because they allow the use of convex optimization techniques in certain non-convex problems. We present known results about DC and locally DC functions, including detailed proofs of important theorems by Hartman and Vesely.

We also investigate the DCA algorithm for optimizing DC functions and implement it to solve the support vector machine problem.

Ruscheweyh-Goyal Derivative Of Fractional Order, Its Properties Pertaining To Pre-Starlike Type Functions And Applications, Ritu Agarwal, G. S. Paliwal

Applications and Applied Mathematics: An International Journal (AAM)

The study of the operators possessing convolution form and their properties is considered advantageous in geometric function theory. In 1975 Ruscheweyh defined operator for analytic functions using the technique of convolution. In 2005, Goyal and Goyal generalized the Ruscheweyh operator to fractional order (which we call here Ruscheweyh-Goyal differential operator) using Srivastava-Saigo fractional differential operator involving hypergeometric function. Inspired by these earlier efforts, we discuss the properties of the Ruscheweyh-Goyal derivative of arbitrary order. We define a class of pre-starlike type functions involving the Ruscheweyh-Goyal fractional derivative and obtain the inclusion relation. Further, we prove that Ruscheweyh-Goyal derivative operator preserve …

Geometric Properties Of Partial Sums Of Generalized Koebe Function, Erhan Deni̇z, Erkan Yalçin

Turkish Journal of Mathematics

The aim of the present paper is to investigate the starlikeness, convexity, and close-to-convexity of some partial sums of the generalized Koebe function. Furthermore, we give some special results related with special cases of $c$ constant. The results, which are presented in this paper, would generalize those in related works of several earlier authors.

General Coefficient Estimates For Bi-Univalent Functions: A New Approach, Oqlah Alrefai, Mohammed Ali

Turkish Journal of Mathematics

We prove for univalent functions $f(z)=z+\sum_{k=n}^{\infty}a_k z^k;(n\geq 2)$ in the unit disk $\mathbb{U}=\{z:\; z