On Integral Operator and Argument Estimation of a Novel Subclass of Harmonic Univalent Functions

Document Type : Research Paper

Authors

Department of mathematics, payame noor university, p.o.box 19395-3697, tehran, iran

10.22034/amfa.2020.1885000.1340

Abstract

Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.

Keywords


[1] Black, F., Scholes, M., The pricing of options and corporate liabilities, J. Political Econom., 1973, 81, P. 637-654.
 
[2] Merton, R.C., Theory of rational option pricing, Bell J. Econom. Manag. Sci., 1973, 4, P. 141-183.
 
[3] Delbaen, F., Schachermayer, W., Handbook of the Geometry of Banach Spaces, vol. 1, Edited by William B. Johnson and Joram Lindenstrauss, 2001, 9, P. 367-392.
 
[4] Harms, P., Stefanovits, D., Affine representations of fractional processes with applications in mathematical finance, Stochastic Processes and their Applications, 2019, 129 (4), P. 1185-1228. Doi: 10.1016/j.spa.2018.04.010.
 
[5] Choquet, G., Sur un type de transformation analytique generalisant la representation conforme et definie au moyen de fonctions harmoniques, Bull. Sci. Math., 1945, 89 (2), P. 156-165.
 
[6] Kneser, H., Losung der Aufgabe 41, Jahresber. Deutsch. Math.-Verein., 1926, 36, P. 123-124.  
 
[7] Lewy, H., On the non-vanishing of the Jacobian in certain one-to-one mappings, Bull. Amer. Math. Sot., 1936, 42, P. 689-692.
 
[8] Rado, T., Aufgabe 41, Jahresber. Deutsch. Math.-Vermin., 1926, 35, P. 49-62.
 
[9] Clunie, J., and Sheil-Small, T., Harmonic univalent functions, Ann. Acad. Aci. Penn. Ser. A I Math., 1984, 9, P. 3-25.
 
[10] Karapinar, E., Mosai, S., Taherinejad, F., A Corporate Perspective on Effect of Asymmetric Verifiability on Investors’ Expectation Differences. Advances in Mathematical Finance and Applications, 2019, 4(4), P. 1-18. Doi: 10.22034/amfa.2019.1869165.1227
 
[11] Farshadfar, Z., Prokopczuk, M., Improving Stock Return Forecasting by Deep Learning Algorithm, Advances in Mathematical Finance and Applications, 2019, 4(3), P. 1-13. Doi: 10.22034/amfa.2019.584494.1173
 
[12] Izadikhah, M., Improving the Banks Shareholder Long Term Values by Using Data Envelopment Analysis Model, Advances in Mathematical Finance and Applications, 2018, 3(2), P. 27-41. Doi: 10.22034/amfa.2018.540829
 
[13] Tripathi, S., Application of Mathematics in Financial Management. Advances in Mathematical Finance and Applications, 2019, 4(2), P. 1-14. Doi: 10.22034/amfa.2019.583576.1169
 
[14] Ahuja, O.P., Jahangiri, J.M., Silverman, H., Convolutions for Special Classes of Harmonic Univalent Functions, Applied Mathematics Letters, 2003, 16, P. 905-909. Doi: 10.1016/S0893-9659(03)90015-2
 
[15] Silverman, H., Harmonic Univalent Functions with Negative Coefficients, Journal of Mathematical Analysis and Applications, 1998, 220, P. 283, 289. Doi: 10.1006/jmaa.1997.5882
 
[16] Ahuja, O.P., Jahangiri, J.M., Certain multipliers of univalent harmonic functions, Applied Mathematics Letters, 2005, 18, P. 1319–1324. Doi: 10.1016/j.aml.2005.02.003
 
[17] Yalçin, S., A new class of Salagean-type harmonic univalent functions, Applied Mathematics Letters, 2005, 18, P. 191–198. Doi: 10.1016/j.aml.2004.05.003
 
[18] Muir, S., Weak subordination for convex univalent harmonic functions, J. Math. Anal. Appl., 2008, 348, P. 862–871. Doi: 10.1016/j.jmaa.2008.08.015
 
[19] Wang, Z-G., Liu, Z-H., Li, Y-C., On the linear combinations of harmonic univalent mappings, J. Math. Anal. Appl., 2013, 400, P. 452–459. Doi: 10.1016/j.jmaa.2012.09.011
 
[20] Li, L., Ponnusamy, S., Disk of convexity of sections of univalent harmonic functions, J. Math. Anal. Appl., 2013, 408, P. 589–596. Doi: 10.1016/j.jmaa.2013.06.021
 
[21] Ho, K-P., Integral operators on BMO and Campanato spaces, Indagationes Mathematicae, 2019, 30 (6), P. 1023–1035. Doi: 10.1016/j.indag.2019.05.007
 
[22] Berra, F., Carena, M., Pradolini, G., Mixed weak estimates of Sawyer type for fractional integrals and some related operators, J. Math. Anal. Appl., 2019, 479 (2), P. 1490–1505. Doi: 10.1016/j.jmaa.2019.07.008
 
[23] Li, B., He, B., Zhou, D., Approximation on variable exponent spaces by linear integral operators, Journal of Approximation Theory, 2017, 223, P. 29-51, Doi:10.1016/j.jat.2017.07.009
 
[24] Bernstein, S.N., D´emonstration du t´eor´eme de Weirerstrass, fond´ee sur le calcul des probabilit´es, Commun. Soc. Math. Kharkow, 1912-1913, 13, P. 1-2.
 
[25] Ruzhansky, M., Sugimoto, M., A local-to-global boundedness argument and Fourier integral operators, J. Math. Anal. Appl., 2019, 473 (2), P. 892-904, Doi: 10.1016/j.jmaa.2018.12.074
 
[26] Grinshpan, A.Z., Estimating the Argument of Some Analytic Functions, journal of approximation theory, 1997, 88 (1), P. 135-138. Doi: 10.1006/jath.1996.3084
 
[27] Cho, N.E., Srivastava, H.M.,  Argument Estimates of Certain Analytic Functions Defined by a Class of Multiplier Transformations, Mathematical and Computer Modelling, 2003, 37 (1-2), P. 39-49. Doi: 10.1016/S0895-7177(03)80004-3 
 
[28] Aouf, M.K., Argument estimates of certain meromorphically multivalent functions associated with generalized hypergeometric function, Applied Mathematics and Computation, 2008, 206 (2), P. 772–780. Doi: 10.1016/j.amc.2008.09.046
 
[29] Cho, N.E., Owa, S., Argument estimates of meromorphically multivalent functions, J. Inequal. Appl., 2000, 5, P. 49–432.
 
[30] Dziok, J., Srivastava, H.M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 1999, 103 (1), P. 1–13. Doi: 10.1016/S0096-3003(98)10042-5
 
[31] Brigo, D., Hanzon, B., On some filtering problems arising in mathematical finance, Insurance: Mathematics and Economics, 1998, 22 (1), P. 53-64. Doi: 10.1016/S0167-6687(98)00008-0
 
[32] Al-Oboudi, F.M., Convolution properties of harmonic univalent functions preserved by some integral operator, Acta Universitatis Apolensis, 2010, 23, P. 139–145.
 
[33] Al-Oboudi, F.M., Al-Amoudi, K.A., Subordination results for classes of analytic functions related to Conic domains defined by a fractional operator, J. Math. Anal. Appl., 2009, 354 (2), P. 412–420. Doi: 10.1016/j.jmaa.2008.10.025
 
[34] Al-Oboudi, F.M., Al-Qahtani, Z.M., On a subclass of analytic functions defined by a new multiplier integral operator, Far East J. Math. Sci., 2007, 25(1), P. 59–72.
 
[35] Izadikhah, M., Saen, RF., Ahmadi, K., How to assess sustainability of suppliers in the presence of dual-role factor and volume discounts? A data envelopment analysis approach, Asia-Pacific Journal of Operational Research, 2017, 34 (03), 1740016, Doi: 10.1142/S0217595917400164
 
[36] Salagean, G.S., Subclasses of analytic functions, Proc. 5th Rom. Finn. Semi. Bucharest, Part 1, Lect. Notes Math., 1983, 1013, P. 362–372.
 
[37] Shuai, L., Peide, L., A new class of harmonic univalent functions by the generalized Salagean operator, WUJNS, 2007, 12(6), P. 965–970. Doi: 10.1007/s11859-007-0044-6
 
[38] Hernández, I., Mateos, C., Núñez, J., Tenorio, A.F., Lie Theory: Applications to problems in Mathematical Finance and Economics, Applied Mathematics and Computation, 2009, 208 (2), P. 446–452. Doi: 10.1016/j.amc.2008.12.025
 
[39] Jahangiri, J.M., Harmonic functions star like in the unit Disk, J. Math. Anal. Appl., 1999, 235 (2), P. 470–477. Doi: 10.1006/jmaa.1999.6377
 
[40] Izadikhah, M., Saen, RF., Roostaee, R., How to assess sustainability of suppliers in the presence of volume discount and negative data in data envelopment analysis?, Annals of Operations Research, 2018, 269 (1-2), 241-267. Doi: 10.1016/j.eswa.2014.08.019
 
[41] Rosy, T., Stephen, B.A., Subramanian, K.G., Jahangiri, J.M., Goodman-Rnning-type harmonic univalent functions, Kyangpook Math. J., 2001, 4(1), P. 45–54.
 
[42] Khalique, C.M., Motsepa, T., Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance, Physica A, 2018, Doi: 10.1016/j.physa.2018.03.053