Papers by Branko Malesevic
Springer optimization and its applications, 2019
In this paper the double-sided TAYLOR's approximations are studied. A short proof of a well-known... more In this paper the double-sided TAYLOR's approximations are studied. A short proof of a well-known theorem on the double-sided TAYLOR's approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such approximations. Then we present some new applications of the double-sided TAYLOR's approximations in the theory of analytic inequalities.
Journal of Science and Arts
This paper considers MEP - Mixed Exponential Polynomials as one class of real exponential polynom... more This paper considers MEP - Mixed Exponential Polynomials as one class of real exponential polynomials. We introduce a method for proving the positivity of MEP inequalities over positive intervals using the Maclaurin series to approximate the exponential function precisely. Additionally, we discuss the relation between MEPs and stratified families of functions from [1] through two applications, referring to inequalities from papers [2] and [3].
arXiv (Cornell University), Jul 18, 2013
Hacettepe journal of mathematics and statistics, Feb 15, 2023
Using the estimations of the even-indexed Bernoulli number and Euler number this paper establishe... more Using the estimations of the even-indexed Bernoulli number and Euler number this paper established some new inequalities for the three functions 2 (sin x) /x + (tan x) /x, (sin x) /x + 2 (tan(x/2)) / (x/2) and 2x/ sin x + x/ tan x bounded by the powers of tangent function.
arXiv (Cornell University), Jun 28, 2023
This paper considers MEP-Mixed Exponential Polynomials as one class of real exponential polynomia... more This paper considers MEP-Mixed Exponential Polynomials as one class of real exponential polynomials. We introduce a method for proving the positivity of MEP inequalities over positive intervals using the Maclaurin series to approximate the exponential function precisely. Additionally, we discuss the relation between MEPs and stratified families of functions from [1] through two applications, referring to inequalities from papers [2] and [3].
arXiv (Cornell University), Dec 19, 2017
In this paper we propose a new method for sharpening and refinements of some trigonometric inequa... more In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens's type.
Applied Mathematics and Computation, Jun 1, 2016
The aim of this paper is to apply an original computation method due to Malešević and Makragić [5... more The aim of this paper is to apply an original computation method due to Malešević and Makragić [5] to the problem of approximating some trigonometric functions. Inequalities of Wilker-Cusa-Huygens are discussed, but the method can be successfully applied to a wide class of problems. In particular, we improve the estimates recently obtained by Mortici [1] and moreover we show that they hold true also on some extended intervals.
arXiv (Cornell University), Jun 11, 2019
In this paper the double-sided TAYLOR's approximations are used to obtain generalisations and imp... more In this paper the double-sided TAYLOR's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
arXiv (Cornell University), Sep 1, 2020
In the paper, we refine and extend Cusa-Huygens inequality by simple functions. In particular, we... more In the paper, we refine and extend Cusa-Huygens inequality by simple functions. In particular, we determine sharp bounds for sin(x)/x of the form (2 + cos(x))/3 − (2/3 − 2/π)Υ(x), where Υ(x) > 0 for x ∈ (0, π/2), Υ(0) = 0 and Υ(π/2) = 1, such that sin x/x and the proposed bounds coincide at x = 0 and x = π/2. The hierarchy of the obtained bounds is discussed, along with a graphical study. Also, alternative proofs of the main result are given.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2022
In this paper, we generalize J. Sándor's results on D'Aurizio's trigonometric inequalities using ... more In this paper, we generalize J. Sándor's results on D'Aurizio's trigonometric inequalities using stratified families of functions.
Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas, Oct 26, 2021
Journal of Inequalities and Applications, Apr 3, 2019
In this paper, we obtain some new inequalities which reveal the further relationship between the ... more In this paper, we obtain some new inequalities which reveal the further relationship between the inverse tangent function arctan x and the inverse hyperbolic sine function sinh-1 x. At the same time, we give the analogue for inverse hyperbolic tangent and inverse sine.
Journal of Mathematical Inequalities, 2022
In this paper, we provide a method to prove an inequality. As applications of the method develope... more In this paper, we provide a method to prove an inequality. As applications of the method developed here, we establish Wilker and Huygens type inequalities for Gauss lemniscate functions, and present sharp inequalities between the inverse hyperbolic tangent and inverse sine functions. We also present sharp inequalities for trigonometric functions.
The Journal of Nonlinear Sciences and Applications, May 16, 2018
In this paper, we propose and prove some generalizations and sharpenings of certain inequalities ... more In this paper, we propose and prove some generalizations and sharpenings of certain inequalities of Wilker's and Shafer-Fink's type. Application of the Wu-Debnath theorem enabled us to prove some double sided inequalities.
arXiv (Cornell University), Jun 11, 2004
In this paper we consider the functional equation for alternating factorial sum and some of its p... more In this paper we consider the functional equation for alternating factorial sum and some of its particular solutions (alternating Kurepa's function A(z) from [18] and function A1(z)). We determine an extension of domain of functions A(z) and A1(z) in the sense of the principal value at point [6], [22]. Using the methods from [6] and [19] we give a new representation of alternating Kurepa's function A(z), which is an analog of Slavić's representation of Kurepa's function K(z) [6], [8]. Also, we consider some representations of functions A(z) and A1(z) via incomplete gamma function and we consider differential transcendency of previous functions too.
arXiv (Cornell University), Aug 31, 2006
In this paper we consider a numerical method for proving a class of analytical inequalities via m... more In this paper we consider a numerical method for proving a class of analytical inequalities via minimax rational approximations. All numerical calculations in this paper are given by Maple computer program.
In this paper some applications of λ-method of Mitrinović-Vasić for obtaining approximations in... more In this paper some applications of λ-method of Mitrinović-Vasić for obtaining approximations in filter design. Some approximations of functions based on cardinal sine functions are given, and also example of an method for obtaining similar approximations for other functions.
2022 30th Telecommunications Forum (TELFOR), Nov 15, 2022
arXiv (Cornell University), Aug 31, 2006
In this article λ-method of Mitrinović-Vasić [1] is applied to improve the upper bound for the ar... more In this article λ-method of Mitrinović-Vasić [1] is applied to improve the upper bound for the arc sin function of L. Zhu [4].
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Papers by Branko Malesevic