Geometric properties of Laplace–Stieltjes integrals

M. M. Sheremeta

Анотація


Геометричні властивості інтегралів Лапласа–Стілтьєса

 

Для інтегралів Лапласа–Стілтьєса введено поняття псевдозірковості та псевдоопуклості. Доведено критерії для псевдозірковості та псевдоопуклості і застосовано їх до вивчення околу функції та згортки функцій.

 

Зразок для цитування: M. M. Sheremeta, “Geometric properties of Laplace – Stieltjes integrals,” Мат. методи та фіз.-мех. поля, 65, No. 3-4, 29–43 (2022), https://doi.org/10.15407/mmpmf2022.65.3-4.29-43


Ключові слова


інтеграл Лапласа–Стілтьєса, псевдозірковість, псевдоопуклість, окіл функції, згортка функцій

Посилання


O. M. Holovata, O. M. Mulyava, M. M. Sheremeta, “Pseudostarlike, pseudoconvex, and close-to-pseudoconvex Dirichlet series satisfying differential equations with exponential coefficients,” Mat. Met. Fiz.-Mekh. Polya, 61, No. 1, 57–70 (2018) (in Ukrainian); English translation: J. Math. Sci., 249, No. 3, 369–388 (2020), https://doi.org/10.1007/s10958-020-04948-1

G. M. Goluzin, Geometric Theory of Functions of a Complex Variable [in Russian], Vol. 26 of Translations of Mathematical Monographs, Amer. Math. Soc., 1969, https://doi.org/10.1090/mmono/026

Yu. F. Korobeinik, N. N. Mavrodi, “Singular points of the Hadamard composition,” Ukr. Mat. Zh., 42, No. 12, 1711–1713 (1990) [in Russian]; English translation: Ukr. Math. J., 42, No. 12, 1545–1547 (1990), https://doi.org/10.1007/BF01060828

O. S. Posiko, “On the abscissa of convergence of the Laplace – Stieltjes integral,” Visn. Lviv. Univ., Ser. Mekh.-Mat., Iss. 53, 123–139 (2004) (in Ukrainian).

O. S. Posiko, O. B. Skaskiv, M. M. Sheremeta, “Estimates of the Laplace – Stieltjes integral,” Mat. Stud., 21, No. 2, 179–186 (2004) (in Ukrainian).

O. Altintaş, Ő. Őzkan, H. M. Srivastava, “Neighborhoods of a class of analytic functions with negative coefficients,” Appl. Math. Lett., 13, No. 3, 63–67 (2000), https://doi.org/10.1016/S0893-9659(99)00187-1

M. K. Aouf, H. Silverman, “Generalizations of Hadamard products of meromorphic univalent functions with positive coefficients,” Demonstratio Mathematica, 41, No. 2, 381–388 (2008), https://doi.org/10.1515/dema-2008-0214

L. Bieberbach, Analytische Fortzetzung, Springer, Berlin, 1955.

J. H. Choi, Y. C. Kim, S. Owa, “Generalizations of Hadamard products of functions with negative coefficients,” J. Math. Anal. Appl., 199, No. 2, 495–501 (1996), https://doi.org/10.1006/jmaa.1996.0157

R. Fournier, “A note on neighborhoods of univalent functions,” Proc. Amer. Math. Soc., 87, No. 1, 117–121 (1983), https://doi.org/10.2307/2044365

B. A. Frasin, M. Darus, “Integral means and neighborhoods for analytic univalent functions with negative coefficients,” Soochow J. Math., 30, No. 2, 217–223 (2004).

A. W. Goodman, “Univalent functions and nonanalytic curves,” Proc. Amer. Math. Soc., 8, No. 3, 598–601 (1957), https://doi.org/10.1090/S0002-9939-1957-0086879-9

V. P. Gupta, “Convex class of starlike functions,” Yokohama Math. J., 32, 55–59 (1984).

J. Hadamard, “La série de Taylor et son prolongement analytique,” Scientia: Phys.-Math., No. 12 (1901).

. J. Hadamard, “Théorème sur les séries entières,” Acta Math., 22, 55–63 (1899), https://doi.org/10.1007/BF02417870

I. S. Jack, “Functions starlike and convex of order alpha,” J. London Math. Soc., s2-3, No. 3, 469–474 (1971), https://doi.org/10.1112/jlms/s2-3.3.469

J.-L. Liu, P. Srivastava, “Hadamard products of certain classes of p-valent starlike functions,” RACSAM Rev. R. Acad. A, 113, No. 3, 2001–2015 (2019), https://doi.org/10.1007/s13398-018-0584-y

M. L. Mogra, “Hadamard product of certain meromorphic univalent functions,” J. Math. Anal. Appl., 157, No. 1, 10–16 (1991), https://doi.org/10.1016/0022-247X(91)90133-K

G. Murugusundaramoorthy, H. M. Srivastava, “Neighborhoods of certain classes of analytic functions of complex order,” J. Inequal. Pure Appl. Math., 5, No. 2, Art. 24 (2004).

M. N. Pascu, N. R. Pascu, “Neighborhoods of univalent functions,” Bull. Aust. Math. Soc., 83, No. 2, 210–219 (2011), https://doi.org/10.1017/S0004972710000468

S. Ruscheweyh, “Neighborhoods of univalent functions,” Proc. Amer. Math. Soc., 81, No. 4, 521–527 (1981), https://doi.org/10.2307/2044151

M. M. Sheremeta, Asymptotical Behavior of Laplace – Stieltjes integral, Vol. 15 of Mathematical Studies Monograph Series, VNTL Publishers, Lviv, 2010.

M. M. Sheremeta, Geometric Properties of Analytic Solutions of Differential Equations, Publ. I. E. Chyzhykov, Lviv, 2019, https://doi.org/10.30970/ms.52.2.138-143

M. M. Sheremeta, “Pseudostarlike and pseudoconvex Dirichlet series of order alpha and type beta,” Mat. Stud., 54, No. 1, 23–31 (2020), https://doi.org/10.30970/ms.54.1.23-31.

H. Silverman, “Neighborhoods of classes of analytic functions,” Far East J. Math. Sci., 3, No. 2, 165–169 (1995).

L. Zalzman, “Hadamard product of shlicht functions,” Proc. Amer. Math. Soc., 19, No. 3, 544–548 (1968), https://doi.org/10.1090/S0002-9939-1968-0224800-8


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