The Open Journal of Mathematical Analysis (OMA) ISSN: 2616-8103 (Print), 2616-8111(Online) is an international research journal dedicated to the publication of original and high quality research papers that treat the mathematical analysis in broad and abstract settings. To ensure fast publication, editorial decisions on acceptance or otherwise are taken within 4 to 12 weeks (three months) of receipt of the paper.
Accepted articles are immediately published online as soon as they are ready for publication. There is one volume containing two issues per year. The issues will be finalized in June and December of every year. The printed version will be published in December of every year. The journal will also publish survey articles giving details of research progress made during the last three decades in a particular area.
Using opoola differential operator, we defined a subclass \(S^{n}_{p}(\lambda,\alpha,\gamma,\delta)\) of the class of multivalent or p-valent functions. Several properties of the class were studied, such as coefficient inequalities, hadamard product, radii of close-to-convex, star-likeness, convexity, extreme points, the integral mean inequalities for the fractional derivatives, and further growth and distortion theorem are given using fractional calculus techniques.
In this paper, we present results of \(\omega\)-order preserving partial contraction mapping generating a nonlinear Schr\”odinger equation. We used the theory of semigroup to generate a nonlinear Schr\(\ddot{o}\)dinger equation by considering a simple application of Lipschitz perturbation of linear evolution equations. We considered the space \(L^2(\mathbb{R}^2)\) and of linear operator \(A_0$ by $D(A_0)=H^2(\mathbb{R}^2)\) and \(A_0u=-i\Delta u\) for \(u\in D(A_0)\) for the initial value problem, we hereby established that \(A_0\) is the infinitesimal generator of a \(C_0\)-semigroup of unitary operators \(T(t)\), \(-\infty<t<\infty\) on \(L^2(\mathbb{R}^2)\).
In this paper, closed forms of the sum formulas \(\sum\limits_{k=0}^{n}kx^{k}W_{k}\) and \(\sum\limits_{k=1}^{n}kx^{k}W_{-k}\) for generalized Tetranacci numbers are presented. As special cases, we give summation formulas of Tetranacci, Tetranacci-Lucas, and other fourth-order recurrence sequences.
This work is devoted to study the global solutions of a class of nonlinear Moore-Gibson-Thompson equation. By applying the Galerkin and compact methods, we derive some sufficient conditions on the nonlinear terms, which lead to the existence and uniqueness of the global solution.
This work is an in-depth study of the class of norm-attainable operators in a general Banach space setting. We give characterizations of norm-attainable operators on involutive stereotype tubes with algebraically connected component of the identity. In particular, we prove reflexivity, boundedness and compactness properties when the set of these operators contains unit balls with involution for the tubes when they are of stereotype category.
In this article we study the existence of periodic and strong solutions of Navier-Stokes equations, in two dimensions, with non-local viscosity.
In this paper we consider the following abstract class of weakly dissipative second-order systems with infinite memory, \(u”(t)+Au(t)-\displaystyle\int_{0}^{\infty} g(s)A^\alpha u(t-s)ds=0,~t>0,\) and establish a general stability result with a very general assumption on the behavior of \(g\) at infinity; that is \(g'(t) \leq – \xi(t) G \left(g(t)\right),~~t \geq 0.\) where \(\xi\) and \(G\) are two functions satisfying some specific conditions. Our result generalizes and improves many earlier results in the literature. Moreover, we obtain our result with imposing a weaker restrictive assumption on the boundedness of initial data used in many earlier papers in the literature such as the one in [1-5]. The proof is based on the energy method together with convexity arguments.
In this paper, we study the initial boundary value problem for a p-biharmonic parabolic equation with logarithmic nonlinearity. By using the potential wells method and logarithmic Sobolev inequality, we obtain the existence of the unique global weak solution. In addition, we also obtain decay polynomially of solutions.
In this paper, we investigate some properties of the \(AP\)-Henstock integral on a compact set and prove that the product of an \(AP\)-Henstock integrable function and a function of bounded variation is \(AP\)-Henstock integrable. Furthermore, we prove that the product of an \(AP\)-Henstock integrable function and a regulated function is also \(AP\)-Henstock integrable. We also define the \(AP\)-Henstock integral on an unbounded interval, investigate some properties, and show similar multiplier properties.
This paper consists of the results about \(\omega\)-order preserving partial contraction mapping using perturbation theory to generate a one-parameter semigroup. We show that adding a bounded linear operator \(B\) to an infinitesimal generator \(A\) of a semigroup of the linear operator does not destroy A’s property. Furthermore, \(A\) is the generator of a one-parameter semigroup, and \(B\) is a small perturbation so that \(A+B\) is also the generator of a one-parameter semigroup.
