On A Subclass of Harmonic Univalent Funtions Associated with the Differential Operator

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    In this paper, a new subclass of harmonic univalent functions in the unit disk  is introduced using a differential operator. Also the coefficient estimates, convolution conditions, extreme points and convex combinations are obtained.

     

     


  • Keywords


    Harmonic;Univalent functions; Differential operator..

  • References


      [1] J. Clunie and T. Sheil – Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. Al. Math., 9 (1984), no. 3, 3-25.

      [2] O.P. Ahuja, Planer harmonic univalent and related mappings, J. Inequal. Pure Appl. Math, 6 (2005), no.4, 122, 1-18.

      [3] J. M. Jahangiri, N. Magesh and C. Murugesan, Certain subclasses of starlike harmonic functions defined by subordination, J. Frac. Cal. Appl., 8 (2017), no.2, 88-100.

      [4] K. Rajya Laxmi and R. Bharavi Sharma, Coefficient Inequalities of Second Hankel Determinants for Some Classes of Bi-Univalent Functions, Mathematics., 2016, 4, 9; doi:10.3390/math4010009

      [5] S. Altinkaya and S. Yalcin, On a Class of Harmonic Univalent Functions Defined by Using a New Differential Operator, Th. Appl. of Math. And Comp. Sci. 6 (2) (2016) 125-133.

      [6] J. M. Jahangiri, G. Murugusundaramoorthy and K. Vijaya, Starlikeness of Ruscheweyh type harmonic univalent functions, J. Indian Acad. Math. 26 (2004), 191-200.

      [7] K. Rajya Laxmi and R. Bharavi Sharma, Second Hankel Determinant coefficients for some subclass of Bi-univalent functions, Global Journal of Pure and Applied Mathematics, vol.11(2) (2015), pp. 89-92.

      [8] K. Thilagavathi, K. Vijaya and N. Magesh, Certain properties of a subclass of harmonic convex functions of complex order defined by multiplier transformations, Malaya J. Math. 4(3) (2016), 362-372.

      [9] H. Silverman and E.M. Silvia, Subclasses of harmonic univalent functions, New Zeal. J. Math. 28 (1999), 275-284.

      [10] R. Bucur, L. Andrei and D. Daniel, Coefficient bounds and Fekete-Szego problem for a class of analytic functions defined by using differential operator. Appl. Math. Sci. 9(2015), 1355-1368.

      [11] S. Porwal and Shivam Kumar, A new subclass of harmonic univalent functions defined by derivative operator, Elect J. Math. Anal. and Appl., 5(1) (2017), 122-134.

      [12] A.L. Pathak, S.B. Joshi, Preeti Dwivedi and R. Agarwal, A subclass of harmonic univalent functions associated with the derivative operator, Hacet. J. Math. and Stat., 41(1) (2012), 47-58.

      [13] R. Bharavi Sharma and B. Ravindar, On a subclass of harmonic univalent functions defined by convolution and integral convolution, International Journal of Pure and Applied Mathematics, vol. 117(7) 2017, pp. 135-145.

      [14] R. Bharavi Sharma and M. Haripriya, On a class of α-convex functions subordinate to a shell shaped region, The Journal of Analysis, vol.25(1) (2017), pp. 99-105.

      [15] J. M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl., 235, (1999), 470-477.

      [16] N. Magesh and S. Mayilvaganan, On a subclass of harmonic convex functions of complex order, Int. J. Math. Sci. 2012, Article ID 496731, page 13.

      [17] N. Magesh and S. Porwal, Harmonic uniformly -starlike functions defined by convolution and integral convolution, Acta Univ. Apulensis Math. Inform, no. 32 (2012), 129-141.

      [18] Sheil-Small. T, Constants for planar harmonic mappings, J. London Math. Soc. 2 (42) (1990), 237-248.

      [19] R. M. Ali, S. K. Lee, V. Ravichandran, and S. Supramaniam, The coefficient functional for transforms of analytic functions, Bull. Iranian Math. Soc. 35(2) (2009), 119-142.

      [20] R. Bharavi Sharma and B. Ravindar, On a subclass of harmonic univalent functions, Journal of Physics: Conf. Series 1000 (2018) 012115, doi: 10.1088/1742-6596/1000/1/012115.


 

View

Download

Article ID: 14507
 
DOI: 10.14419/ijet.v7i3.3.14507




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.