New classes of harmonic meromorphic multivalent starlike functions in Janowski domain

Volume 24, Issue 3, pp 216--224 http://dx.doi.org/10.22436/jmcs.024.03.03

Publication Date: February 23, 2021 Submission Date: December 14, 2020 Revision Date: December 26, 2020 Accteptance Date: January 03, 2021

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 979 Downloads
• 2164 Views

Authors

Timilehin Gideon Shaba - Department of Mathematics , University of Ilorin, P. M. B. 1515, Ilorin, Nigeria. Bakhtiar Ahmad - Government Degree College Mardan, 23200 Mardan, Pakistan. Muhammad Ghaffar Khan - Institute of Numerical Sciencies, Kohat University of Science and Technology, Kohat, Pakistan. Zabidin Salleh - Department of Mathematics, Faculty of Ocean Engineering Technology and Informatics , Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia. Wali Khan Mashwani - Institute of Numerical Sciencies, Kohat University of Science and Technology, Kohat, Pakistan. Shahid Khan - Institute of Numerical Sciencies, Kohat University of Science and Technology, Kohat, Pakistan.

Abstract

In this article some applications of harmonic analysis are discussed in the field of Geometric Function Theory in the form of a new class of meromorphic multivalent functions. A differential operator for these function have been used to define classes of meromorphic multivalent functions in association with Janowski functions in symmetric points. Various geometric properties like sufficiency criteria, growth theorem, convex combination, weighted mean for these functions have been evaluated for this newly defined class.

Share and Cite

Keywords

• Multivalent function
• harmonic meromorphic function
• Janowski function
• starlike functions
• subordination

MSC

•  30C45
•  30C50

References

• [1] O. P. Ahuja, Planar harmonic univalent and related mappings, J. Inequal. Pure Appl. Math., 6 (2005), 18 pages
  • View Article
  • MathSciNet


• [2] O. P. Ahuja, J. M. Jahangiri, Errata to: "Multivalent harmonic starlike functions", Ann. Univ. Mariae Curie-Skłodowska Sect. A, 55 (2001), 1--13
  • View Article
  • MathSciNet


• [3] O. P. Ahuja, J. M. Jahangiri, Multivalent meromorphic harmonic functions, Adv. Stud. Contemp. Math. (Kyungshang), 7 (2003), 179--187
  • View Article
  • MathSciNet


• [4] A. Aleman, A. Constantin, Harmonic maps and ideal fluid flows, Arch. Ration. Mech. Anal., 204 (2012), 479--513
  • View Article
  • MathSciNet


• [5] H. A. Al-zkeri, F. M. Al-Oboudi, On a class of harmonic starlike multivalent meromorphic functions, Int. J. Open Probl. Complex Anal., 3 (2011), 68--81
  • View Article
  • MathSciNet


• [6] M. Arif, O. Barkub, H. M. Srivastava, S. Abdullah, S. A. Khan, Some Janowski type Harmonic q-starlike functions associated with symmetrical points, Mathematics, 8 (2020), 16 pages
  • View Article
  • MathSciNet


• [7] D. Bshouty, W. Hengartner, M. Naghibi-Beidokhti, p-valent harmonic mappings with finite Blaschke dilatations, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 53 (1999), 9--26
  • MathSciNet
  • Google Scholar


• [8] R. Chand, P. Singh, On certain schlicht mappings, Indian J. Pure Appl. Math., 10 (1979), 1167--1174
  • View Article
  • MathSciNet


• [9] J. Clunie, T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math., 9 (1984), 3--25
  • View Article
  • MathSciNet


• [10] O. Constantin, M. J. Martın, A harmonic maps approach to fluid flows, Math. Ann., 369 (2017), 1--16
  • View Article
  • MathSciNet


• [11] J. Dziok, On Janowski harmonic functions, J. Appl. Anal., 21 (2015), 99--107
  • View Article
  • MathSciNet


• [12] S. Elhaddad, H. Aldweby, M. Darus, On a subclass of harmonic univalent functions involving a new operator containing q-MittagLeffler function, Int. J. Math. Comput. Sci., 14 (2019), 833--847
  • View Article
  • MathSciNet


• [13] J. M. Jahangiri, Coefficient bounds and univalence criteria for harmonic functions with negative coefficients, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 52 (1998), 57--66
  • View Article
  • MathSciNet


• [14] J. M. Jahangiri, Harmonic meromorphic starlike functions, Bull. Korean Math. Soc., 37 (2000), 291--301
  • View Article
  • MathSciNet


• [15] J. M. Jahangiri, H. Silverman, Meromorphic Univalent Harmonic Functions with Negative Coefficients, Bull. Korean Math. Soc., 36 (1999), 763--770
  • View Article
  • MathSciNet


• [16] A. Juma, Study of harmonic multivalent meromorphic functions by using generalized hypergeometric functions, J. Nonlinear Anal. Optim., 2 (2011), 367--372
  • View Article
  • MathSciNet


• [17] M. G. Khan, B. Ahmad, T. Abdeljawad, Applications of a differential operator to a class of harmonic mappings defined by MittagLeffer functions, AIMS Math., 5 (2020), 6782--6799
  • View Article
  • MathSciNet


• [18] M. G. Khan, B. Ahmad, N. E. Cho., Properties of harmonic mappings associated with polylogrithm functions, Applied Mathematics E-Notes, (), Accepted
  • Google Scholar


• [19] M. G. Khan, B. Ahmad, M. Darus, W. K. Mashwani, S. Khan, On Janowski Type Harmonic Meromorphic Functions with respect to Symmetric Point, J. Funct. Spaces, 2021 (2021), 5 pages
  • View Article
  • MathSciNet


• [20] ] M. G. Khan,M. Darus, B. Ahmad, G. Murugusundaramoorty, R. Khan, N. Khan, Meromorphic starlike functions with respect to symmetric points, Int. J. Anal. Appl., 18 (2020), 1037--1047
  • View Article
  • MathSciNet


• [21] H.-G. Li, Some properties of certain meromorphic multivalent close-to-convex functions, Miskolc Math. Notes, 21 (2020), 249--259
  • View Article
  • MathSciNet


• [22] S. Li, H. Tang, L. Ma, E. Ao, A new class of harmonic multivalent meromorphic functions, Bull. Math. Anal. Appl., 7 (2015), 20--30
  • View Article
  • MathSciNet


• [23] G. Murugusundaramoorthy, Starlikeness of multivalent meromorphic harmonic function, Bull. Korean Math. Soc., 40 (2003), 553--564
  • View Article
  • MathSciNet


• [24] I. R. Nezhmetdinov, A sharp lower bound in the distortion theorem for the Sakaguchi class, J. Math. Anal. Appl., 242 (2000), 129--134
  • View Article
  • MathSciNet


• [25] M. Ozawa, An elementary proof of the Bieberbach conjecture for the sixth coefficient, Kodai Math. Sem. Rep., 21 (1969), 129--132
  • View Article
  • MathSciNet


• [26] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan, 11 (1959), 72--75
  • View Article
  • MathSciNet


• [27] F. M. Sakar, H. O. Guney, New subclass of multivalent meromorphic harmonic functions defined by a new generalized al-boudi differential operator,, World Appl. Sci. J., 20 (2012), 1696--1703
  • View Article
  • Google Scholar


• [28] T. N. Shanmugam, C. Ramachandran, V. Ravichandran, Fekete-Szegő problem for subclasses of starlike functions with respect to symmetric points, Bull. Korean Math. Soc., 43 (2006), 589--598
  • View Article
  • MathSciNet


• [29] T. Shiel-Small, Constants for planar harmonic mappings, J. London Math. Soc., 42 (1990), 237--248
  • View Article
  • MathSciNet


• [30] H. Silverman, Harmonic univalent functions with negative coeffcients, J. Math. Anal. Appl., 220 (1998), 283--289
  • View Article
  • Google Scholar


• [31] J. Thangamani, On starlike functions with respect to symmetric points, Indian J. Pure Appl. Math., 11 (1980), 392--405
  • View Article
  • MathSciNet


• [32] Z.-G. Wang, Some subclasses of close-to-convex and quasi-convex functions, Mat. Vesnik, 59 (2007), 65--73
  • View Article
  • MathSciNet


• [33] Z.-G. Wang, C.-Y. Gao, S.-M. Yuan, On certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points, J. Math. Anal. Appl., 322 (2006), 97--106
  • View Article
  • MathSciNet


• [34] A. K. Yadav, Harmonic multivalent meromorphic functions defined by an integral operator, J. Appl. Math. Bioinform., 2 (2012), 99--114
  • View Article
  • Google Scholar