Research Article
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On the Analytical Determination of Geometric Characterizations of Analytic Functions

Year 2023, Volume: 4 Issue: 1, 9 - 15, 31.01.2023
https://doi.org/10.54974/fcmathsci.1094167

Abstract

As it is known, there are many sufficient conditions for the classification complex functions of one variable f(z), which are analytic and univalent in the open unit disc U = {z ∈ C ∶ SzS < 1}, and are also normalized with f(0) = 1 − f′(0) = 0 which are also known as normalization conditions. In this sense, the main goal of present article is to derive some special sufficient conditions for f(z) to be starlike of order 2−r and convex of order 2−r in U , with r is a positive integer.

References

  • Akyar A., A new subclass of certain analytic univalent functions associated with hypergeometric functions, Turkish Journal of Mathematics, 46(1), 145-156, 2022.
  • Duren P.L., Univalent Functions, Springer Science, Business Media, Vol. 259, 2001.
  • Goodman A.W., Univalent Functions, Polygonal Publishing House, Vol. I Vol. II, 1983.
  • Guo L., Wang Y., Liu J., On the starlikeness for certain analytic functions, International Journal of Mathematical Research, 1(2), 21-25, 2012.
  • Jack I.S., Functions starlike and convex of order α, Journal of the London Mathematical Society, 2(3), 469-474, 1971.
  • Noor K.I., On Close-to-Convex and Related Functions, Ph.D. Thesis, University of Wales, Swansea, UK, 1972.
  • Noor, K.I., On quasi-convex functions and related topics, International Journal of Mathematics and Mathematical Sciences, 10(2), 241-258, 1978.
  • Nunokawa M., Aydoğan M., Kuroki K., Yildiz I., Owa S., Some properties concerning close-toconvexity of certain analytic functions, Journal of Inequalities and Applications, 245, 2012.
  • Owa S., Saitoh H., Srivastava H.M., Yamakawa R., Geometric properties of solutions of a class of differential equations, Computers and Mathematics with Applications, 47(10-11), 1689-1696, 2004.
  • Pommerenke C., Univalent Functions, Vandenhoeck and Ruprecht, 1975.
  • Singh R., Singh S., Some sufficient conditions for univalence and starlikeness, Colloquium Mathematicum, 47(2), 309-314, 1982.
  • Yildiz I., Akyar A., An analytical investigatıon on starlikeness and convexity properties for hypergeometric functions, Turkish Journal of Mathematics, 44(4), 1453-1465, 2022.
Year 2023, Volume: 4 Issue: 1, 9 - 15, 31.01.2023
https://doi.org/10.54974/fcmathsci.1094167

Abstract

References

  • Akyar A., A new subclass of certain analytic univalent functions associated with hypergeometric functions, Turkish Journal of Mathematics, 46(1), 145-156, 2022.
  • Duren P.L., Univalent Functions, Springer Science, Business Media, Vol. 259, 2001.
  • Goodman A.W., Univalent Functions, Polygonal Publishing House, Vol. I Vol. II, 1983.
  • Guo L., Wang Y., Liu J., On the starlikeness for certain analytic functions, International Journal of Mathematical Research, 1(2), 21-25, 2012.
  • Jack I.S., Functions starlike and convex of order α, Journal of the London Mathematical Society, 2(3), 469-474, 1971.
  • Noor K.I., On Close-to-Convex and Related Functions, Ph.D. Thesis, University of Wales, Swansea, UK, 1972.
  • Noor, K.I., On quasi-convex functions and related topics, International Journal of Mathematics and Mathematical Sciences, 10(2), 241-258, 1978.
  • Nunokawa M., Aydoğan M., Kuroki K., Yildiz I., Owa S., Some properties concerning close-toconvexity of certain analytic functions, Journal of Inequalities and Applications, 245, 2012.
  • Owa S., Saitoh H., Srivastava H.M., Yamakawa R., Geometric properties of solutions of a class of differential equations, Computers and Mathematics with Applications, 47(10-11), 1689-1696, 2004.
  • Pommerenke C., Univalent Functions, Vandenhoeck and Ruprecht, 1975.
  • Singh R., Singh S., Some sufficient conditions for univalence and starlikeness, Colloquium Mathematicum, 47(2), 309-314, 1982.
  • Yildiz I., Akyar A., An analytical investigatıon on starlikeness and convexity properties for hypergeometric functions, Turkish Journal of Mathematics, 44(4), 1453-1465, 2022.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Alaattin Akyar 0000-0003-4759-8313

Publication Date January 31, 2023
Published in Issue Year 2023 Volume: 4 Issue: 1

Cite

19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.