Prof. Dr. Gradimir V. Milovanović

Prof. Dr. Gradimir V. Milovanović is a Serbian mathematician renowned for his contributions to approximation theory, numerical analysis, and orthogonal polynomials. He has authored numerous papers and books, advancing research in these fields.

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Research Interests

Orthogonal Polynomials and Systems

Study of families of polynomials that are mutually orthogonal with respect to specific inner products and weight functions-ranging from classical to non-classical measures on domains like the real line, unit circle, and semicircle-primarily for advancing Gaussian quadrature rules in numerical integration, moment-preserving spline approximations, extremal problems, numerical differentiation, and the summation of slowly convergent series.

Interpolation, Quadrature Processes and Integral Equations

Study of and advancing convergent interpolation methods for algebraic and trigonometric polynomials using optimal node systems and tools like orthogonal polynomials, developing Gaussian-type quadrature formulas with error estimates for numerical integration of highly oscillating functions, and creating numerical solutions for Fredholm integral equations of the second kind based on polynomial interpolation to ensure convergence in weighted uniform norms.

Approximations by Polynomials and Splines

Study of and development of shape-preserving methods and algorithms for interpolating or approximating univariate functions and discrete data, ensuring the retention of key geometric properties such as monotonicity, positivity, and convexity.

Polynomials (Extremal Problems, Inequalities, Zeros)

Study of and analyzing key results in polynomial theory, including optimization challenges like maximizing or minimizing polynomial functionals, deriving inequalities such as Markov-Bernstein types to bound derivatives and values, and examining the distribution, location, and properties of polynomial roots.

Inequalities

Study of mathematical inequalities, particularly those of Markov-Bernstein type, applied to extremal problems, polynomial zeros, approximation theory, and numerical integration.

Publications

Textbooks

Total

Mathematics

G.V. Milovanović

D.D. Joksimović

R.Ž. Đorđević

Kriminalističko-policijska akademija, Beograd, 11000, Serbia

2015

(Second Edition 2019)

VIII+304 pp.

(Serbian)

Systems of Differential Equations

D.Ć. Dolićanin-Đekić

I.A. Soloviev

R.Ž. Đorđević

G.V. Milovanović

State University of Novi Pazar, Novi Pazar, Serbia

2013

IV+145 pp.

(Serbian)

Mathematics I

Linear Algebra, Polynomials, Analytic Geometry

M.A. Kovačević

G.V. Milovanović

R.Ž. Đorđević

Sven, Niš, 18000, Serbia

2012

VIII+302, pp.

(Serbian)

Applications of Linear and Integer Programming

P.S. Stanimirović

G.V. Milovanović

I.M. Jovanović

University of Niš, Faculty of Science and Mathematics, Niš, 18000, Serbia

2008

X+298 pp.

(Serbian)

Operations Research

Lj.M. Kocić

G.V. Milovanović

S.D. Marinković

University of Niš, Faculty of Electronic Engineering, Niš, 18000, Serbia

2008

X+204 pp.

(Serbian)

Numerical Methods in Computational Engineering

G.V. Milovanović

Ð. R. Đorđević

University of Niš, Faculty of Civil Engineering and Architecture, Niš, 18000, Serbia

2007

X+180 pp.

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Books & Proceedings Edited

Total

Mihailo Petrović Alas: Life, Work, Times

On the Occasion of the 150th Anniversary of his Birth

G.V. Milovanović

S. Pilipović

Ž. Mijajlović

Serbian Academy of Sciences and Arts, Belgrade, 11000, Serbia

2019

Analytic Number Theory, Approximation Theory, and Special Functions

In Honor of Hari M. Srivastava

G.V. Milovanović

Th.M. Rassias

Springer, Gewerbestrasse 1, Cham, Zug, 6330, Switzerland

2014

XI, 880 p.

Symposium on Approximation, Scientific Computation and Applications "ASCA-2012"

G.V. Milovanović

AIP Conference Proceeedings, Melville, New York, United States of America

2012

In: Numerical Analysis and Applied Mathematics (ICNAAM 2012)

Vol. 1479 (2012), p. 1041

DOI 10.1063/1.4756323

Proceedings of the Eight Symposium of Mathematics and its Applications

Papers from the Symposium held at the Electrical Engineering Faculty, Department of Mathematics, Timisoara, România, November 4 – 7, 1999

N. Boja

G.V. Milovanović

P. Corsini

P. Gavruta

Politehnica Timisoara, Bul. St. Univ., Timisoara, Romania

1999

Recent Progress in Inequalities

A volume dedicated to Professor D. S. Mitrinović, Mathematics and Its Applications

G.V. Milovanović

Kluwer Academic Publishers, Dordrecht, Netherlands

1998

In: Vol. 430

XII + 532 pp.

MR1611734 (98k:00021)

978-90-481-4945-2

Numerical Methods and Approximation Theory III

Papers from the Conference held at the University of Niš, Niš, August 18 – 21, 1987

G.V. Milovanović

University of Niš, Faculty of Electronic Engineering, Niš, 18000, Serbia

1987

XII+436 pp.

MR 89c: 65007

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Monographs

Total

Quadrature Formulae With Multiple Nodes

(Draft version)

G.V. Milovanović

M.M. Spalević

M.S. Pranić

World Scientific Publishing Co., Singapore – New Jersey – London – Hong Kong, Singapore

2026

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

Mathematical Analysis and Its Applications

R.B. Gardner

N.K. Govil

G.V. Milovanović

Elsevier/Academic Press, London, United Kingdom of Great Britain and Northern Ireland

2022

XVIII+424 pp.

Numerical Analysis and Approximation Theory

Introduction to Numerical Processes and Solving Equations

G.V. Milovanović

Zavod za udžbenike, Belgrade, 11000, Serbia

2014

(Serbian)

Special Classes of Polynomials

G.B. Đorđević

G.V. Milovanović

University of Niš, Faculty of Technology, Leskovac, Serbia

2014

Extremal Problems and Inequalities for Polynomials

G.V. Milovanović

Zavod za udžbenike, Belgrade, 11000, Serbia

2012

(Serbian)

Interpolation Processes - Basic Theory and Applications

Springer Monographs in Mathematics

G. Mastroianni

G.V. Milovanović

Springer – Verlag, Berlin - Heidelberg, Germany

2008

XIV+444 pp.

MR2457729 (2009i:41001)

978-3-540-68346-9

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Book chapters

Total

Iterative processes and integral equations of the second kind

S. Micula

G.V. Milovanović

Springer, Gewerbestrasse 1, Cham, Zug, 6330, Switzerland

2023

In: Matrix and Operator Equations and Applications (M. S, Moslehian, ed.)

pp. 661 – 711

Dedekind and Hardy type sums and trigonometric sums induced by quadrature formulas

G.V. Milovanović

Y. Simsek

Springer, Gewerbestrasse 1, Cham, Zug, 6330, Switzerland

2020

In: Trigonometric Sums and Their Applications (A.M. Raigorodskii, M.Th. Rassias, eds.)

pp. 183 – 228

978-3-030-37903-2

Best constants for Poincare-type inequalities in W_1^n(0,1)

A. Guessab

G.V. Milovanović

Springer, Gewerbestrasse 1, Cham, Zug, 6330, Switzerland

2019

In: Differential and Integral Inequalities (D. Andrica, Th.M. Rassias, eds.), Springer Optimization and Its Applications, Vol. 151

pp. 391 – 402

978-3-030-27406-1

The Serbian school of mathematics

from Mihailo Petrović to the Shanghai list

G.V. Milovanović

M. Mateljević

M. Albijanić

Serbian Academy of Sciences and Arts, Belgrade, 11000, Serbia

2019

In: Mihailo Petrović Alas: Life, Work,Times - On the Occasion of the 150th Anniversary of his Birth (S. Pilipović, G.V. Milovanović, Ž. Mijajlović, eds.)

pp. 65 – 92

Some reverse Hölder type inequalities involving (k,s)–Riemann-Liouville fractional integrals

M. Tomar

P. Agarwal

S. Jain

G.V. Milovanović

Springer, Gewerbestrasse 1, Cham, Zug, 6330, Switzerland

2017

In: Functional Analysis in Interdisciplinary Applications. FAIA 2017 (T. Kalmenov, E. Nursultanov, M. Ruzhansky, M. Sadybekov, eds.), Springer Proceedings in Mathematics & Statistics, Vol. 216

pp. 302 – 311

978-3-319-67052-2

Summation formulas of Euler-Maclaurin and Abel-Plana: old and new results and applications

G.V. Milovanović

Springer, Gewerbestrasse 1, Cham, Zug, 6330, Switzerland

2017

In: Progress in Approximation Theory and Applicable Complex Analysis – In the Memory of Q.I. Rahman (N.K. Govil, R.N. Mohapatra, M.A. Qazi, G. Schmeisser, eds.)

pp. 429 – 461

978-3-3199-49240-1

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Refereed Journals

Total

A gradient projection algorithm based on the normal-S iterative algorithm: Convergence analysis and machine learning application

M. Ertürk

F. Gürsoy

E. Hacioğlu

G.V. Milovanović

Optimization Letters, Springer Nature, Berlin, London, New York, Heidelberg , Germany

2025

18 pp

Closed-form formulas of two Gauss hypergeometric functions of specific parameters

G.V. Milovanović

F. Qi

Journal of Mathematical Analysis and Applications, Elsevier, PO Box 211, Amsterdam, 1000 AE, Netherlands

2025

534(2), 129024

Convergence-Equivalent DF and AR Iterations with Refined Data Dependence: Non-Asymptotic Error Bounds and Robustness in Fixed-Point Computations

K. Doğan

E. Hacioğlu

F. Gürsoy

M. Ertürk

G.V. Milovanović

Axioms, MDPI AG, Grosspeteranlage 5, Basel, Basel, 4052, Switzerland

2025

14(10), 738

20 pp

Exploring the potential of inertial type algorithms in solving coincidence point/value problems: Theoretical analysis and practical applications

A. Keten Çopur

E. Hacioğlu

F. Gürsoy

G.V. Milovanović

Faculty of Science and Mathematics (FILOMAT), Višegradska 33, P.O. Box 224, Niš, 18000, Serbia

2025

39(29)

10205 – 10233

Flexible and efficient iterative solutions for general variational inequalities in real Hilbert spaces

E. Hacioğlu

M. Ertürk

G.V. Milovanović

Axioms, MDPI AG, Grosspeteranlage 5, Basel, Basel, 4052, Switzerland

2025

24(2)

264 – 276

DOI: 10.30546/1683-6154.24.2.2025.264

Gauss quadrature rules for integrals involving weight functions with variable exponents and an application to weakly singular Volterra integral equations

C. Allouch

G.V. Milovanović

IMA Journal of Numerical Analysis, Oxford University Press, Great Clarendon Street, Oxford, OX2 6DP, United Kingdom of Great Britain and Northern Ireland

2025

45(6)

1 – 28