Volume 5 (2021) Issue 1

Author(s): Curtis Holliman1, Logan Hyslop1
1Department of Mathematics, The Catholic University of America, Washington, DC 20064, USA
Abstract:

The Cauchy problem for a higher order modification of the nonlinear Schrödinger equation (MNLS) on the line is shown to be well-posed in Sobolev spaces with exponent \(s > \frac{1}{4}\). This result is achieved by demonstrating that the associated integral operator is a contraction on a Bourgain space that has been adapted to the particular linear symbol present in the equation. The contraction is proved by using microlocal analysis and a trilinear estimate that is shown via the \([k; Z]\)-multiplier norm method developed by Terence Tao.

Author(s): W. L. Otae1, N. B. Okelo1, O. Ongati1
1Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya
Abstract:

In this paper, we give characterizations of orthogonality conditions in certain classes of normed spaces. We first consider Range-Kernel orthogonality in norm-attainable classes then we characterize orthogonality conditions for Jordan elementary operators.

Author(s): Christophe Chesneau1
1Université de Caen Normandie, LMNO, Campus II, Science 3, 14032, Caen, France
Abstract:

Copulas played a key role in numerous areas of statistics over the last few decades. In this paper, we offer a new kind of trigonometric bivariate copula based on power and cosine functions. We present it via analytical and graphical approaches. We show that it may be used to create a new bivariate normal distribution with interesting shapes. Subsequently, the simplest version of the suggested copula is highlighted. We discuss some of its relationships with the Farlie-Gumbel-Morgensten and simple polynomial-sine copulas, establish that it is a member of a well-known semi-parametric family of copulas, investigate its dependence domains, and show that it has no tail dependence.

Author(s): Ahmed Ali Al-Gonah1, Ahmed Ali Atash2
1Department of Mathematics, Faculty of Science, Aden University, Aden, Yemen
2Department of Mathematics, Faculty of Education Shabwah, Aden University, Aden, Yemen
Abstract:

Recently, many extensions of some special functions are defined by using the extended Beta function. In this paper, we introduce a new generalization of extended Gegenbauer polynomials of two variables by using the extended Gamma function. Some properties of these generalized polynomials such as integral representation, recurrence relation and generating functions are obtained.

Author(s): Bashir Danladi Garba1,2, Sirajo Lawan Bichi2
1Department of Mathematics, Kano University of Science and technology, Wudil Kano, Nigeria
2Department of Mathematical Sciences, Bayero University Kano, Nigeria
Abstract:

In this paper, a hybrid of Finite difference-Simpson’s approach was applied to solve linear Volterra integro-differential equations. The method works efficiently great by reducing the problem into a system of linear algebraic equations. The numerical results shows the simplicity and effectiveness of the method, error estimation of the method is provided which shows that the method is of second order convergence.

Author(s): Kuldeep Kaur Shergill1, Sukhwinder Singh Billing1
1Department of Mathematics, Sri Guru Granth Sahib World University, Fatehgarh Sahib-140407(Punjab), India
Abstract:

In the present paper, we define a class of non-Bazilevic functions in punctured unit disk and study a differential inequality to obtain certain new criteria for starlikeness of meromorphic functions.

Author(s): Mawia Osman1, Zengtai Gong2, Altyeb Mohammed Mustafa1,3
1College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, P.R. China.
2College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, P.R. China
3Department of Applied Mathematics, Faculty of Mathematical Science, University of Khartoum, Khartoum, Sudan.
Abstract:

In this paper, the reduced differential transform method (RDTM) is applied to solve fuzzy nonlinear partial differential equations (PDEs). The solutions are considered as infinite series expansions which converge rapidly to the solutions. Some examples are solved to illustrate the proposed method.

Author(s): Timilehin Gideon Shaba1
1Department of Mathematics, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria.
Abstract:

In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with \(q\)-derivative operator; both \(f\) and \(f^{-1}\) are \(m\)-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients \(|\rho_{m+1}|\) and \(|\rho_{2m+1}|\) are found in this study. Also certain special cases are indicated.

Author(s): Taieb Hamaizia1
1Laboratory of Dynamical Systems and Control, Department of Mathematics and Informatics, Oum El Bouaghi University, 04000, Algeria.
Abstract:

The purpose of this paper is to prove a fixed point theorem for \(C\)-class functions in complete \(b\)-metric spaces. Moreover, the solution of the integral equation is obtained using our main result.

Author(s): Khaled Hleili1,2
1Preparatory Institute for Engineering Studies of Kairouan, Department of Mathematics, Kairouan university, Tunisia.
2Department of Mathematics, Faculty of Science, Northern Borders University, Arar, Saudi Arabia.
Abstract:

In this work, we establish \(L^p\) local uncertainty principle for the Hankel-Stockwell transform and we deduce \(L^p\) version of Heisenberg-Pauli-Weyl uncertainty principle. Next, By combining these principles and the techniques of Donoho-Stark we present uncertainty principles of concentration type in the \(L^p\) theory, when \(1\)<\(p\leqslant2\). Finally, Pitt’s inequality and Beckner’s uncertainty principle are proved for this transform.