A New General Multivalent Integral Operator

G. Thirupathi

doi:https://doi.org/10.14445/22315373/IJMTT-V65I8P510

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 8 | Year 2019 | Article Id. IJMTT-V65I8P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I8P510

A New General Multivalent Integral Operator

G. Thirupathi

Abstract

n this paper, we define a new multivalent integral operator for certain subclass of analytic functions in the open unit disc U . We obtain some interesting properties for this integral operator.

Keywords

analytic function, multivalent function, integral operator, starlike and convex functions.

References

[1] J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. of Math. (2), 17 , no. 1, 12—22, 1915.
[2] D. Breaz and N. Breaz, “Two integral operators,” Studia Universitatis Babes-Bolyai, Mathematica, Cluj-Napoca, 47, no.3, pp. 13— 19, 2002.
[3] D. Breaz, S. Owa, N. Breaz, A new integral univalent operator, Acta Univ. Apulensis Math. Inform. no. 16 , 11—16, 2008.
[4] B. A. Frasin, Family of analytic functions of complex order, Acta Math. Acad. Paedagog. Nyh?zi. (N.S.), 22, no. 2, 179—191, 2006.
[5] B. A. Frasin, Convexity of integral operators of $p-$valent functions, Mathematical and Computer Modelling, An International Journal, 51, no.5-6, p.601—605, 2010.
[6] R. J. Libera, Univalent  -spiral functions, Canad. J. Math. 19, 449—456, 1967.
[7] S. S. Miller, P. T. Mocanu, M. O. Reade, Starlike integral operators, Pacific J. Math. , 79, no. 1, 157—168, 1978.
[8] M. A. Nasr, M. K. Aouf, Starlike function of complex order, J. Natur. Sci. Math., 25, no. 1, 1—12, 1985.
[9] S. Owa, On uniformly convex functions, Math. Japon, 48, no. 3, 377—384, 1998.
[10] G. S. Salagean, Subclasses of univalent functions, Complex Analysis - Fifth Romanian Finish Seminar, Bucharest, 1, 362—372, 1983.
[11] G Saltik, E Deniz, E Kadioglu, Two new general $p$-valent integral operators, Math. Comput. Modelling, 52,, no. 9-10, 1605—1609, 2010.
[12] G. M. Shenan, T. O. Salim, M. S. Marouf, A certain class of multivalent prestarlike functions, involving the Srivastava-Saigo-Owa fractional integral operator, Kyungpook Math. J. 44, no. 3, 353—362, 2004.
[13] L. Stanciu, D. Breaz, Some properties of a general integral operator, Bull. Iranian Math. Soc. 40, no. 6, 1433—1439, 2014.
[14] P. Wiatrowski, The coefficients of a certain family of holomorphic functions, (Polish) Zeszyty Nauk. Uniw. Lódz. Nauki Mat. Przyrod. Ser. II No. 39, Mat. 75—85, 1971.
[15] D. Yang, S. Owa, Properties of certain $p-$ valently convex functions, IJMMS, 41, 2603—2608, 2003.

Citation :

G. Thirupathi, "A New General Multivalent Integral Operator," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 8, pp. 97-103, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I8P510