On a Generalized Subclass of p-Valent Meromorphic Functions by Defined q-Derivative Operator

Subject Areas : Financial Mathematics

Mohammad Hassan  Golmohammadi ¹ (Department of Mathematics, Payame Noor University, P. O. Bax: 19395 - 3697, Tehran, Iran)
Shahram  Najafzadeh ² (Department of Mathematics, Payame Noor University, P. O. Box: 19395 - 3697, Tehran, Iran)
Mohammad Reza  Forutan ³ (Department of Mathematics, Payame Noor University, P. O. Box: 19395 - 3697, Tehran, Iran)

Received: 2020-11-21 Accepted : 2021-01-22 Published : 2021-10-01

Keywords:

References:

[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. Doi: 10.2307/3003143

 

[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] Dibachi, H., Behzadi, M.H., Izadikhah, M., Stochastic Modified MAJ Model for Measuring the Efficiency and Ranking of DMUs, Indian Journal of Science and Technology, 2015, 8(8), P. 1-7, Doi: 10.17485/ijst/2015/v8iS8/71505

[5] 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.

 

[6] 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] Dibachi, H., Behzadi, M.H., Izadikhah, M., Stochastic multiplicative DEA model for measuring the efficiency and ranking of DMUs under VRS technology, Indian Journal of Science and Technology, 2014, 7 (11), P. 1765–1773. Doi: 10.17485/ijst/2014/v7i11.19

 

[11] 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

 

[12] 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

 

[13] 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

 

[14] 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

 

[15] 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

 

[16] Gasper, G., Rahman, M., Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, 1990.

 

[17] Izadikhah, M., Using goal programming method to solve DEA problems with value judgments, Yugoslav Journal of Operations Research, 2016, 24 (2), P. 267–282. Doi: 10.2298/YJOR121221015I

 

[18] Raina, K.R., Srivastava, H.M., Inclusion and neighborhoods properties of some analytic and multivalent functions, J. In-equal. Pure and Appl. Math, 2006, 7(1), P. 1-6.

 

[19] Ruscheweyh, S., Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 1981, 81(4), P. 521-527. Doi: 10.2307/2044151

 

[20] Ahmad, B., Arif, M., On a generalized subclass of meromorphically p-valent close to convex functions in q-analogue, In. J. Maps Math., 2019, 2, P. 148-158.

 

[21] Abelman, S., Selvakumaran, K.A., Rashidi, M.M., Purohit, SD., Subordination conditions for a class of non-Bazilevic type definde by using fractional q-calculus operators, Facta Univ. Ser. Math.Inform., 2017, 32, P. 255-267. Doi: 10.22190/FUMI1702255A

 

[22] Aldweby, H., Darus, M., A subclass of harmonic univalent functions associated with q-analogue of Dziok Srivastava operator, ISRN Math. Anal., 2013, 6, P. 382-312. Doi: 10.1155/2013/382312

 

[23] Jackson, FH., On q-functions and a certain difference operator, Trans. Royal Soc. Edinburgh,1909, 46 (2), P. 253-281. Doi: 10.1017/S0080456800002751

 

[24] Izadikhah, M., Farzipoor Saen, R., Ranking sustainable suppliers by context-dependent data envelopment analysis. Ann Oper Res, 2020, 293, P.607–637, Doi: 10.1007/s10479-019-03370-4

[25] Juma, A., Abdulhussain, M., Al-Khafaji, S., Certain subclass of pp-valent meromorphic Bazilevi'{c} functions defined by fractional q-calculus operators, International Journal of Nonlinear Analysis and Applications, 2018, 9(2), P. 223-230. Doi: 10.22075/ijnaa.2018.13163.1681

 

[26] Purohit, S.D., A new class of multivalently analytic functions associated with fractional q-calculus operators, Frac. Differ. Calc., 2012, 2 (2), P. 129-138. Doi:10.7153/fdc-02-10

 

[27] 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[14] M. L.

 

[28] Mogra, M.L., Reddy, T.R., Juneja, O.P., Meromorphic multivalent functions with positive coefficients, Bulletin of the Australian Mathematical Society, 1985, 32(2), P. 61–176. Doi:10.1017/S0004972700009874

 

[29] Altintas, O., Owa, S., Neighborhoods of certain analytic functions with negative coefficients, Internat. J. Math. Math. Sci., 1996, 19, P. 797-800. Doi: 10.1155/S016117129600110X

 

[30] Tone, K., Toloo, M., Izadikhah, M., A modified slacks-based measure of efficiency in data envelopment analysis, European Journal of Operational Research, 2020, 287 (2), P. 560-571, Doi: 10.1016/j.ejor.2020.04.019.

[31] Goodman, A.W., Univalent function and analytic curves, Proc. Amer. Math. Soc., 1957, 8 (3), P. 598-601. Doi: 10.2307/2033525

 

[32] Lashin, A.Y., On certain subclasses of meromorphically p-valent functions, Demonstratio Math., 2008, 61, P. 371-380. Doi: 10.1515/dema-2008-0213