Prof. Dr. Eman Samir Bhaya

1-            A study on approximations of bounded measurable functions with some discrete series in Lp spaces p<1, M.Sc. thesis, Baghdad University (2000).

2-            Operators for best approximation and best one sided approximation in Lp, p<1,Babylon University Journal for pure and applied mathematics, vol10,number 3, 723-727, (2005).

3-            One sided approximation and saturation problem for some trigonometric operators in Lp, p>0, Babylon University Journal for pure and applied mathematics, vol9,number 3, 847-852, (2004).

4-            A characterization of the best and best one sided algebraic approximation in Lp[0,1](0<p)Babylon University Journal for pure and applied mathematics, vol 10, number 3, 2005., 749-750.

5-            Convergence of periodic functions by interpolating polynomials, Babylon University Journal for pure and applied mathematics, vol 7, number 3, 2002., 967-974.

6-            Approximation of positive and monotone functions, Journal of College of Education, Al Mustanseria University, vol.7, 8- 16,(2002).

7-            Direct and inverse theorems for best multi-approximation in Lp, p>1,Maths and Physics J. vol. 17 (5),1-8, (2002).

8-            On the constrained and unconstrained approximation, Ph.D. thesis, Baghdad University(2003).

9-            Orders of coaproximation of functions by algebraic polynomials, Al- Qadysia Journal for pure science-vol.9, no.1, 338-345.(2004).

11-           Weak copositive approximation and Whitney theorem in

Lp,p<1, Jordan Journal of applied science , Natural science, vol.8,no.2,51-58, (2006).

12-           Simultaneous convex polynomial and spline approximation, Journal of Babylon University for pure and applied sciences, vol.13, no. 3, 1045-1051. (2006).

13-           Almost copositive polynomial approximation in Lp[-1,1],p<1 The first conference on mathematical sciences (2006), Zarqa private University Jordan 52-57..

14-           Asymptotic behavior of derivatives of near best approximation polynomials, J. Basah Research (sciences), vol. 33, no.3, 54-59.sep (2007).(2005)

15-           Approximation of 3-monotone functions by 3-monotone functions in Lp spaces. The second scientific conference in Kufa University(2009).

16-           A saturation theorem and negative theorem for monotone approximation. Journal of College of Education, Babylon University, for the second scientific conference vol.3.10- 14.(2008).

17-           Lp,p<1Polynomial approximation on Cube. Uruk Journal,vol1.141-146,( papers of the first scientific conference in College of science Al Muthana University9-10 October(2007).

18-           Lp,p<1Polynomial approximation on Cube. Uruk Journal,vol1.141-146,( papers of the first scientific conference in College of science Al Muthana University9-10 October(2007).

19-           Estimates for comonotone polynomial approximation in Lp.

The second conference of Mathematical science (CMS 2008), Zarqa private University Jordan 438-444.

20-           Inverse and direct theorems for monotone approximation The

first scientific conference for pure and applied sciences12-13 March (2008). 180-175. Kufa University.

21-           Interpolating operators for multi approximation. Journal of mathematics and statistics. 6(3):2333-239,2010.USA.

22-           Probability and Functional analysis , Babylon Journal for natural sciences, a special volume for the papers of the first scientific conference for college of education Babylon       University, 17-18 February vol.2, 72-77.(2007).

23-           A normed Orlices Classes and Spaces, Babylon Journal for natural sciences, a special volume for the papers of the first scientific conference for college of education Babylon University, 17-18 February vol.2, 85-87.(2007).

24-           One-sided and co-onesided approximation, European Journal of Scientific Research, vol44, Issue 2.

25-             Coconvex polynomial approximation42-57,(2009) . Journal of Al- Qadysia for mathematics and computer sciences, A special volume for The first scientific conference for mathematics and computer science, Al Qadisia University 27-28, August , 2008.

26-   Direct estimation for multivariate polynomial approximation. J. of Kerbala University, Scientific Journal vol.5, no.2, 136-142, (2007).

27-   The rate of co approximation of monotone functions in Lp, p<1. Al Kufa Journal . ISSN 1994-2168, vol. 8, no.1, 2007, 30-46.

28-   Convex approximation by polynomials and piecewise polynomials

(KAJ) Kurdistan Academicians Journal, March, (2007), 5(1) part A, 103-108.

29-   On k-monotone approximation in Lp Journal of Kufa for Mathematics and Computer Faculty of Mathematics and Computer Sciences. Issn. 2076-1171.vol. 1,no.1p. 54-64.

30- Free knot spline approximation of k-monotone functions for feed forward neural

networks. Australian Journal of Basic and Applied Sciences, 2966- AJBAS 12-8-2010.

31.  A saturation and inverse theorem for co positive approximation in Lp for 0<p<1. Accepted in the Journal of Babylon University, 978,8- 8-2010.

32.  On Lorentz space. Introduced to the Journal of Babylon University. 2010

33.  Orders of co approximations of functions by polynomials. The third conference of Mathematical science (CMS 2010), Zarqa private University Jordan 600-605.

34.  On Jacksons theorem. International Journal of Science and Technology, vo. 1, no. 6, 2011.

35A modulus of smoothness in terms of fractional order. International Journal of Contemporary Mathematical Sciences. Vol. 7. No. 37. Pp. 1807-1817.2012.

36.   Estimates in terms of partial moduli of smoothness. International

Journal of Contemporary Mathematical Sciences. Vol. 7. No. 37. Pp. 1819-1829.

37.   Positivity Preserving Multiapproximation. American Journal of Scientific and industrial research 3(6), 2012.

38.   Simultaneous approximation by complex polynomial. Int. Journal of Mathematical analysis. Vol. 7, no. 36, 1803-1808, 2013. IF. 0.2

39.   Stability and density of periodic points of Lp, spaces,0<p<1. Int. Journal of Mathematical analysis. Vol. 7, no. 34, 1673-1684, 2013.

IF. 0.2.

40. Results on comonotone approximation. The Int. Journal of mathematical Archive, 2013, Icv. 5.09.234-242, 4(7), 2013.

41.   Some results on comonotone approximation. Accepted in Journal of Babylon University, 2013.

.42 التنمية المستدامة. و ينشر في مجلة اتحاد الجامعات العربية / كلية الهندسة/ جامعة بغداد.

43.  Some properties of semi dynamical system generated by Von Forester Losata type. 7(38), 1863-1868.

44.  Complex operators for complex approximation. Ijma. Info 4(81), 2013,1-10.

45.  Estimates for approximation of 3-monotone functions. Ijma. Info. 5910), 2014,1-5.

46.  Converse result on copositive approximation in 𝐿𝜓,𝑝(𝐼), 𝑝 < 1.

International research journal of Scientific findings 1(6), 229-236.

47.  Coconvex approximation of unbounded function in Lp spaces II.

International research journal of Scientific findings. 1(4), 153-162. 2014.

48.  Coconvex approximation of unbounded function in Lp spaces. International research journal of Scientific findings.1(3), 0087-0098. 2014.

49.  Simultaneous monotone multiapproximation. International journal of mathematical analysis. 8(24). 1169-1177. 2014.

50.  Negative theorem for monotone bivariate approximation. International journal of mathematical analysis. 8(24). 1179-1185.

51.    Piecewise 3-monotone approximation on 𝑳𝑷-spaces for 𝑷 < 𝟏.

journal

of Babylon University, 24(4), 2016.Acepted in 15-6-2015

52.  Degree of Approximation by Taylor Operator of Functions in 𝑰𝒑(𝑼)

Space.

for    𝒑 < 𝟏. Accepted in the journal of Babylon University, may, 2015.v.24,no. 3, 2016.

53.      Equivalence   between   K-functional            and             r-th        modulus            of smoothness for neural networks.

Accepted in the journal of Babylon University, may, 2015.

54.   Lp direct theorem for exponential neural networks. Accepted in the University of

Babylon journal, in 14-6-2015, and will published in v. 24, n. 4 in 2016.

55.   Nearly exponential approximation for neural networks. Journal of University of Babylon. N. 1, vol. 26,2018.

56.  Spherical approximation on unit sphere. Journal of Babylon University. V26,n2,2018. To apper.

57.   The essential order of Lp,p<1 approximation using regular neural network. . Journal of Babylon University. V26,n1,2018, to appear.

58.    on the mixed rth modulus of smoothness. Journal of Babylon

University. V26,n1,2018, to appear.

59.  Lp, p<1 Approximation Using Radial Basis Function Neural Networks on Ordered Vector Space.

60.  On monotone rational approximation.nJournal of Babylon Universityn Pure and Applied Sciences. N. 1, vol. 26m 2018.

61.   Jacobi Weighted Moduli of Smoothness for Approximation by Neural Networks Approximation. Journals of University of Babylon. V27, n. 2019.

62.  A new modulus of smoothness for uniform approximation. Journals of University of Babylon. V26, N.8, 2018.

63.   A new modulus of smoothness of k monotone functions in Lp spaces for p<1 . Journal of Engineering and Applied Sciences, issn,1816-949X.

v. 14, n. 12-13,Jun 2019.

64.   Whitney Multiapproximation> journal of University of Babylon for Pure and Applied Siences, vol26, no7, 2018.

65.      Constructive Approch of Neural Network Approximation of Trigonometric Activation Function. Journal of Engineering and Applied Sciences. Vol.15, no 1.

66.      Stechin Marchaud inequality in terms of Nural Networks Approximation in Lp spaces for 0<p<1. 2nd international conference of Kerbala University, College of Education for Pure Sciences.

67.  Lp Approximation of Functions on Graphs.                                                  الدولي المؤتمر وقائع في نشر

الرابع حول معامل التاثير العربي 24-21 يونيو 2019

68.  Approximation of functions in Lp spaces for p<1, using radial basis function neural networks. J of University of Babylon for Pure and applied Sciences, v.27, n.3, 2019.

69.    Best Neural Simultaneous Approximation 2-normed Lp spaces, Indonesian Journal of Electrical Engineering and Computer Science, v.14,

n. 2, 2019, issn. 2502-4752.

72.    Sobolev Inequalities for Functions on Graphs, Bhaya, ES, Flaih, Z. Journal of Physics: Conference Seriesthis link is disabled, 2021, 1804(1), 012132

73 . Approximation of fourier series in terms of functions in L p spaces for 0 <p <1

Aboud, SM, Bhaya, ES International Journal of Nonlinear Analysis and Applicationsthis link is disabled, 2021, 12(2), pages 897–911

74.    Sobolev Inequalities for Functions on GraphsBhaya, ES, Flaih, Z. Journal of Physics: Conference Seriesthis link is disabled, 2021, 1804(1), 012132

75.   Nearly Monotone Neural Approximation with Quadratic Activation Function Almurieb, HA, Bhaya, ES Journal of Physics: Conference Seriesthis link is disabled, 2021, 1804(1), 012098

76.   Moduli of Smoothness for Weighted L p ,0 <p <1 Approximation Sharba, ZA, Bhaya, ES Journal of Physics: Conference Seriesthis link is disabled, 2021, 1804(1), 012081

77.   Best neural simultaneous approximation Almurieb, HA, Bhaya, ES Indonesian Journal of Electrical Engineering and Computer Sciencethis link is disabled, 2020, 20(3), pages 1584–1590

78.   L P , ∞> P ≥ 1 Simultaneous Approximation Bhaya, ES, Abdoul Khaleq, AH IOP Conference Series: Materials Science and Engineeringthis link is disabled, 2020, 928(4), 042001

79.   Trigonometric Neural Networks L p , p<1 Approximation Bhaya, ES, Abd Al-Sadaa, ZH Journal of Physics: Conference Seriesthis link is disabled, 2020, 1591(1), 012060

80.    SoftMax Neural Best Approximation Almurieb, HA, Bhaya, ES IOP Conference Series: Materials Science and Engineeringthis link is disabled, 2020, 871(1), 012040

81.   L_p_ approximation by ReLU neural networks Bhaya, ES, Sharba, ZA Karbala International Journal of Modern Sciencethis link is disabled, 2020, 6(4), pages 414–419

82.    Finite fourier coefficients is best approximation to f∈ l(P,α,β) Kazem, HN, Bhaya, ES Journal of Advanced Research in Dynamical and Control Systemsthis link is disabled, 2020, 12(5), pages 193–199

83.   𝐿𝑝, APPROXIMATION OF FUNCTIONS ON GRAPHS Abdul Jalil M. Khalaf and Eman S Bhaya, Jour of Adv Research in Dynamical & Control Systems, Vol. 11, 10-Special Issue, 2019

84.    Monotone Approximation by Quadratic Neural Network of Functions in L p Spaces for p<1, Iraqi Journal of Science, 2020, Vol. 61, No. 4, pp: 870-874 DOI: 10.24996/ijs.2020.61.4.20.

85.   Does Math Destroyed the Jurassic Park? Journal of University of Babylon for Pure and Applied Sciences, Vol. (28), No. (3): 2020 Online ISSN: 2312-8135, Print ISSN: 1992-0652.

86.   Best neural simultaneous approximation. Indonesian Journal of Electrical Engineering and Computer Science Vol. 20, No. 3, December 2020, pp. 1584~1590 ISSN: 2502-4752, DOI: 10.11591/ijeecs.v20.i3.pp1584-1590.

87.   LP , ∞ > P ≥ 1 Simultaneous Approximation. 2nd International Scientific Conference of Al-Ayen University (ISCAU-2020) IOP Conf. Series: Materials Science and Engineering 928 (2020) 042001 IOP Publishing doi:10.1088/1757-899X/928/4/042001.

88.   Trigonometric Neural Networks Lp , p<1. FISCAS 2020 Journal of Physics: Conference Series 1591 (2020) 012060 IOP Publishing doi:10.1088/1742-6596/1591/1/012060.

89.   Sobolev Inequalities for Functions on Graphs. ICMAICT 2020 Journal of Physics: Conference Series 1804 (2021) 012132 IOP Publishing doi:10.1088/1742- 6596/1804/1/012132.

90.   L_p_ Appr L_p_ Approximation b ximation by ReLU Neural Networks. Karbala International Journal of Modern Science: Vol. 6 : Iss. 4 , Article 9.

91.   Moduli of Smoothness for Weighted Lp ,0 < p < 1 Approximation. ICMAICT 2020 Journal of Physics: Conference Series 1804 (2021) 012081 IOP Publishing doi:10.1088/1742- 6596/1804/1/012081.

92.   Finite Fourier Coefficients is Best Approximation to f𝐿𝑝𝛼𝛽. Jour of Adv Research in Dynamical & Control Systems, Vol. 12, No. 5, 2020.

93.   A Look at Sobolev Spaces on Graphs. 2nd International Scientific Conference of Al-Ayen University (ISCAU-2020) IOP Conf. Series: Materials Science and Engineering 928 (2020) 042011 IOP Publishing doi:10.1088/1757-899X/928/4/042011.

94.   Nearly Monotone Neural Approximation with Quadratic Activation Function. ICMAICT 2020 Journal of Physics: Conference Series 1804 (2021) 012098 IOP Publishing doi:10.1088/1742-6596/1804/1/012098.

95.   SoftMax Neural Best Approximation. The First International Conference of Pure and Engineering Sciences (ICPES2020) IOP Conf. Series: Materials Science and Engineering 871 (2020) 012040 IOP Publishing doi:10.1088/1757-899X/871/1/012040.

96.   Degree of best approximation in terms of weighted DT moduli of smoothness. Doi: 10.5373/JARDCSI/V1214/20201419.

97.   Shape preserving approximation using convex smooth piecewise polynomials for functions in Lp quasi normed spaces. Int. J. Nonlinear Anal. Appl. 13 (2022) 1, 3363-3370 ISSN: 2008-6822 (electronic) http://dx.doi.org/10.22075/ijnaa.2022.6096.

98.   “Piecewise Convex L_p,0<p<1. 1st International Conference on Advanced Research in Pure and Applied Science”, which will be held at College of Science / Al- Muthanna

University, Iraq during 24-25 March, 2021. Your paper will be published online by AIP Conference Proceedings (ISSN: 0094-243X).

99.  . VDUNKL WEIGTED INVERS THEOREMS APPROXMATI OF FUNCTIONES.

NeuroQuantology.

100.    A Modified Ostrowski Inequality with Random Variable Application on Lp [a, b], 0 < p < 1,Spaces. International Journal of Mechanical Engineering. ISSN: 0974-5823 Vol. 7 No. 3 March, 2022.

101.    Approximation of Expectation and Variance on [𝑎, 𝑏] Interval, with Probability Density Function in 𝐿𝑝 [𝑎, 𝑏], 0 < 𝑝 < 1. ISSN: 0974-5823 Vol. 7 No. 3 March, 2022 International Journal of Mechanical Engineering.

102.    An application of a modified Chebyshev inequality. Conference AIP. 2022

103.    Inequalities for Expectation, Variance and Dispersion. AIP conference Proceeding.2022

104.    Saturation Problems for Positive Linear Approximation of Function in Quasi Normed spaces. n International Journal of Health Sciences (IJHS). 2022. 6(S3), 12070–12077.

105.    COLINEAR APPROXIMATION IN TERMS OF GENERALIZAL WEIGHTED MODULUS OF

SMOOTHESS IN LP SPACES. ISSN: 0974-5823 Vol. 7 No. 2 February, 2022 International Journal of Mechanical Engineering.

106.    Ditzain-Totik modulus of smoothness for the fractional derivative of functions in Lp space of the partial neural network. Int. J. Nonlinear Anal. Appl. 13 (2022) 1, 3305-3317 ISSN: 2008-6822 (electronic) 

107.    Weighted approximation using neural network in terms of fractional modulus of smoothness of fractional derivative. Int. J. Nonlinear Anal. Appl. 13 (2022) 1, 3381-3394 ISSN: 2008-6822 (electronic)