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Examining the Function of Meromorphic with Using the Linear Convolution Operator

Year 2021, , 609 - 616, 01.03.2021
https://doi.org/10.21597/jist.807358

Abstract

In this study, it is mentioned that meromorphic functions are univalent functions that
are analytical everywhere. Complex analytical transformations were investigated by mentioning the
necessary form for f (z) to have meromorphic function. It is a function that satisfies the condition
  0 hz  . For analytic functions of f and g in the D unit disk, ()fz shows the meromorphic
function class with P and subclasses of the P meromorphic analytical function class using the
subordination principle between functions with the help of Hadamard product and linear operators. In
this way proves is provided.

References

  • Alexander JW, 1915. Functions which map the interior of the unit circle upon simple regions, Annals of Math. 17, 15-22.
  • Cho NE, Owa S, 2004. Partial Sums of certain meromorphic functions, J. Inequal. Pure and Appl. Math., 5(2) Art. 30.
  • Cho NE, Kim IH, 2007. Inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function, Appl. Math. Compu., 187 (1), 115 121.
  • Dziok J, Srivastava HM, 2003. Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14 (1) ,7-18.
  • Gonchar AA, Havin VP, Nikolski NK, 2001. Complex Analysis I. Springer-Verlag, pp 4, Newyork.Goodman A W, 1983. Univalent functions, Vol. I, Mariner Publ. Co., Tampa, FI..
  • Krantz SG, 1999. Handbook of Complex Variables, , Birkhuser, Boston, MA.
  • Liu J, Owa S, 1998. On certain meromorphic p-valent functions, Taiwanese J. Math. 2(1) , pp. 107-110.
  • MacGregor TH, Thomas HA, 1974/75. Subordination for convex functions of order . J. London Math. Soc. (2) 9, 530-536.
  • Marx A, 1936. Untersuchungen ¸ber schlichte Funktionen, Math. Ann. 107, 40-67.
  • Miller SS, Mocanu PT, 1985. On some classes of first order differential subordinations, Michigan Math. J. , 32 ,185-195.
  • Miller J, 1970. Convex meromorphic mappings and related functions, Proc. Amer. Math. Soc., 25 , 220-228.
  • Mogra L, 1991. Hadamard product of certain meromorphic univalent functions, J. Math. Anal. Appl., 157 ,10-16.
  • Nevanlinna R, 1921. über die konforme Abbildung von Sterngebieten, Ofvers. Finska 58 Vet. Soc. Förh., 53 (A), Nr. 6.
  • Nunokawa M, Ahuja OP, 2001. On meromorphic starlike and convex functions, Indian Pure Appl. Math., 32(7), 1027-1032.
  • Pommerenke Ch, 1963. On meromorphic starlike functions. Pacific J. Math. 13 221-235.
  • Royster WC, 1963. Meromorphic Starlike, Trans. Amer. Math. Soc. Vol. 107, No. 2 , pp. 300-308.
  • Srivastava HM, Owa S, 1986. A certain one parameter additive family of operators defined on analytic functions, Journal of mathematıcal analysıs and applıcatıons 118, 80-87.
  • Strohhacker E, 1933. Beitrage zur Theorie der schlichten Funktionen, Math. Z. 37, 356-380.

Examining the Function of Meromorphic with Using the Linear Convolution Operator

Year 2021, , 609 - 616, 01.03.2021
https://doi.org/10.21597/jist.807358

Abstract

In this study, it is mentioned that meromorphic functions are univalent functions that
are analytical everywhere. Complex analytical transformations were investigated by mentioning the
necessary form for f (z) to have meromorphic function. It is a function that satisfies the condition
  0 hz  . For analytic functions of f and g in the D unit disk, ()fz shows the meromorphic
function class with P and subclasses of the P meromorphic analytical function class using the
subordination principle between functions with the help of Hadamard product and linear operators. In
this way proves is provided.

References

  • Alexander JW, 1915. Functions which map the interior of the unit circle upon simple regions, Annals of Math. 17, 15-22.
  • Cho NE, Owa S, 2004. Partial Sums of certain meromorphic functions, J. Inequal. Pure and Appl. Math., 5(2) Art. 30.
  • Cho NE, Kim IH, 2007. Inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function, Appl. Math. Compu., 187 (1), 115 121.
  • Dziok J, Srivastava HM, 2003. Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14 (1) ,7-18.
  • Gonchar AA, Havin VP, Nikolski NK, 2001. Complex Analysis I. Springer-Verlag, pp 4, Newyork.Goodman A W, 1983. Univalent functions, Vol. I, Mariner Publ. Co., Tampa, FI..
  • Krantz SG, 1999. Handbook of Complex Variables, , Birkhuser, Boston, MA.
  • Liu J, Owa S, 1998. On certain meromorphic p-valent functions, Taiwanese J. Math. 2(1) , pp. 107-110.
  • MacGregor TH, Thomas HA, 1974/75. Subordination for convex functions of order . J. London Math. Soc. (2) 9, 530-536.
  • Marx A, 1936. Untersuchungen ¸ber schlichte Funktionen, Math. Ann. 107, 40-67.
  • Miller SS, Mocanu PT, 1985. On some classes of first order differential subordinations, Michigan Math. J. , 32 ,185-195.
  • Miller J, 1970. Convex meromorphic mappings and related functions, Proc. Amer. Math. Soc., 25 , 220-228.
  • Mogra L, 1991. Hadamard product of certain meromorphic univalent functions, J. Math. Anal. Appl., 157 ,10-16.
  • Nevanlinna R, 1921. über die konforme Abbildung von Sterngebieten, Ofvers. Finska 58 Vet. Soc. Förh., 53 (A), Nr. 6.
  • Nunokawa M, Ahuja OP, 2001. On meromorphic starlike and convex functions, Indian Pure Appl. Math., 32(7), 1027-1032.
  • Pommerenke Ch, 1963. On meromorphic starlike functions. Pacific J. Math. 13 221-235.
  • Royster WC, 1963. Meromorphic Starlike, Trans. Amer. Math. Soc. Vol. 107, No. 2 , pp. 300-308.
  • Srivastava HM, Owa S, 1986. A certain one parameter additive family of operators defined on analytic functions, Journal of mathematıcal analysıs and applıcatıons 118, 80-87.
  • Strohhacker E, 1933. Beitrage zur Theorie der schlichten Funktionen, Math. Z. 37, 356-380.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Hasan Şahin 0000-0002-5227-5300

Publication Date March 1, 2021
Submission Date October 8, 2020
Acceptance Date December 14, 2020
Published in Issue Year 2021

Cite

APA Şahin, H. (2021). Examining the Function of Meromorphic with Using the Linear Convolution Operator. Journal of the Institute of Science and Technology, 11(1), 609-616. https://doi.org/10.21597/jist.807358
AMA Şahin H. Examining the Function of Meromorphic with Using the Linear Convolution Operator. Iğdır Üniv. Fen Bil Enst. Der. March 2021;11(1):609-616. doi:10.21597/jist.807358
Chicago Şahin, Hasan. “Examining the Function of Meromorphic With Using the Linear Convolution Operator”. Journal of the Institute of Science and Technology 11, no. 1 (March 2021): 609-16. https://doi.org/10.21597/jist.807358.
EndNote Şahin H (March 1, 2021) Examining the Function of Meromorphic with Using the Linear Convolution Operator. Journal of the Institute of Science and Technology 11 1 609–616.
IEEE H. Şahin, “Examining the Function of Meromorphic with Using the Linear Convolution Operator”, Iğdır Üniv. Fen Bil Enst. Der., vol. 11, no. 1, pp. 609–616, 2021, doi: 10.21597/jist.807358.
ISNAD Şahin, Hasan. “Examining the Function of Meromorphic With Using the Linear Convolution Operator”. Journal of the Institute of Science and Technology 11/1 (March 2021), 609-616. https://doi.org/10.21597/jist.807358.
JAMA Şahin H. Examining the Function of Meromorphic with Using the Linear Convolution Operator. Iğdır Üniv. Fen Bil Enst. Der. 2021;11:609–616.
MLA Şahin, Hasan. “Examining the Function of Meromorphic With Using the Linear Convolution Operator”. Journal of the Institute of Science and Technology, vol. 11, no. 1, 2021, pp. 609-16, doi:10.21597/jist.807358.
Vancouver Şahin H. Examining the Function of Meromorphic with Using the Linear Convolution Operator. Iğdır Üniv. Fen Bil Enst. Der. 2021;11(1):609-16.