In the present study, firstly, some algebraic inequalities are proved, which will be used later. By making use of these relations, some evaluations are found related the gaps between norm and numerical radius, spectral radius and Crawford number for diagonal block operator matrices on the infinite direct sum of Hilbert spaces. Later on, the gaps between some spectral characteristic numbers (operator norm, lower and upper bounds of spectrum set and numerical radius) of the infinite direct sum of Hilbert space operators relatively to the same spectral characteristics of the coordinate operators are investigated. Then, the obtained results are supported by applications. The open problem posed by Demuth in 2015 and the works of Kittaneh and his researcher group in this area had an important effect on the formation of the subject discussed in this study.
In this paper, we study the complexity of p-adic continued fractions of a rational number, which is the p-adic analogue of the Lame's theorem. We calculate the length of Browkin expansion, and the length of Schneider expansion. Also, some numerical examples have been given.
In this paper, we study the complexity of p-adic continued fractions of a rational number, which is the p-adic analogue of the theorem of Lame. We calculate the length of Browkin expansion, and the length of Schneider expansion. Also, some numerical examples have been given.
In this paper, some essential inequalities are established for the quadratic function of bounded variation by using 7-step kernel. Some previous results are recaptured. Applications for quadrature rule and probability density function are also provided.
This research is focusing on the extremum of a given function which involves triangle functions. We collect some typical examples from ordinary high school mathematics teaching and demonstrate several typical mistakes which were usually posed by ordinary high school students usually and analyze the reasons for the errors. These results will be used to help ordinary high school students to well understand AM-GM inequalities and related applications for maximum and minimum values of triangle type functions.
In the paper under consideration, we will discuss integral inequalities by the way of fractional integral operators for generalized convex functions. For fractional integral operators, a new identity is established and some results of Hermite-Hadamard type inequalities are achieved. This fractional operator have been used to derive a new generalization of the Hermite-Hadamard inequality. In the previous papers the author used the definition of k-fractional conformable integral inequalities and we used the definition of katugampola fractional integrals in this paper. In this paper, we have given a best appropriate definition for fractional integral operators.
This work considers the use of Adam Bashforth-Moulton method and Milne Simpson method to solve second order ordinary differential equation with initial value problem and to compare solution with the exact solution, to solve that we first convert the equation to two set of first order differential equation by order reduction method, then we use a single step method for approximation of initially orders which are required to start the linear multistep method. The result show that the numerical solutions are in good agreement with the exact solution. The result show that Adam Bashforth-Moulton method is better than Milne Simpson method in solving differential equation of second order.
In this paper, we define k-order Mersenne numbers inspired the Mersenne numbers. Then, we give some interesting properties such as generating function and sum of the first m terms of these numbers. Also, we give excellent results of the k-order Mersenne numbers. We introduce the matrix representation and obtain the k-order Mersenne matrix.
One of the fundamental problem of the Spectral Theory of Linear Operators is to determine of the geometric place of the spectrum of the given operator and calculate the spectral and numerical radii of this operator. Other important problem in this theory is to explained the situation the spectral (numerical) radius is equal or not to operator norm. The only known way to calculate the spectral radius to date is the classical Gelfand formula, which often presents great technical challenges. Also, there is not yet a method of calculating the numerical radius for an operator. It should be noted that the finding the numerical range and numerical radius means maximally localizing the spectrum of an operator. The main purpose of this paper is to determine the relations gaps between operator norm and spectral and numerical radii of the tensor product operators associated with the compatible gaps of coordinate operators.
In the paper, by using the properties of Schur m-power convex function, we discuss Schur m-power convexity of a new class of symmetric functions where i1, i2, â¦, ir are non-negative integers, and p â N+. We obtain that is Schur m-power convex for m ⤠0 and Schur m-power concave for m ⥠p. We also give a counter example to illustrate is neither Schur convex nor Schur concave for p>1. As applications, a Klamkin-Newman type inequality and some analytic inequalities are derived.
In this paper, we establish integral inequalities of Hermite-Hadamard type for multiplicatively h -preinvex functions. We also obtain some new inequalities involving multiplicative integrals by using some properties of preinvex and multiplicatively h -preinvex functions.
In 2011, E. Karapinar et al. [12] proved some common fixed point theorems for four weakly compatible self-maps in complete partial metric spaces. In this paper, we extend these theorems using E.A. property and (CLR)-property in complete partial metric spaces.
