[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.22771/nfaa.2022.27.04.06

DIFFERENTIAL INEQUALITIES ASSOCIATED WITH CARATHÉODORY FUNCTIONS

In Hwa, Kim (Department of Economics and International Business, Sam Houston State University)
Nak Eun, Cho (Department of Applied Mathematics, Pukyong National University)

Publication Information

Nonlinear Functional Analysis and Applications / v.27, no.4, 2022 , pp. 773-784 More about this Journal

Abstract

The purpose of the present paper is to estimate some real parts for certain analytic functions with some applications in connection with certain integral operators and geometric properties. Also we extend some known results as special cases of main results presented here.

Keywords

Caratheodory function; analytic functions; starlike functions; integral operator;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

Reference
Cited By KSCI

1	E. Bazilevic, On a case of integrability in guadratures of Lowner-Kwfurew equations, Mat. Sb., 37(79) (1955), 471-476.
2	S.D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135 (1969), 429-446. DOI
3	C. Caratheodory, Uber den variabilitatsbereich der coeffizienten von potenzreihen, die gegebene werte nicht annehmen, Math. Ann. 64(1) (1907), 95-115. DOI
4	C. Caratheodory, Uber den variabilitatsbereich der fourier'schen konstanten von positiven harmonischen funktionen, Rend. Circ. Mat. Palermo, 32 (1911), 193-217. DOI
5	I.H. Kim and N.E. Cho, Sufficient conditions for Caratheodory functions, Comput. Math. Appl., 59 (2010), 2067-2073. DOI
6	V. Kumar and S.L. Shukla, On p-valeut starlike functions with referenceto the Bernardi integral operator, Bull. Austral. Math. Soc., 30 (1984), 37-43. DOI
7	O.S. Kwon and Y.J. Sim, Sufficient conditions for Caratheodory functions and applications to univalent functions, Math. Slovaca, 69(5) (2019), 1065-1076. DOI
8	R.J. Libera, some classes of regular univalent functions, Proc. Amer. Math. Soc., 16 (1965), 755-758. DOI
9	A.E. Livingstin, On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc., 17 (1966), 352-357. DOI
10	T.H. MacGrGregor, A subordination for convex functions of order α, J. London Math. Soc., 9(2) (1975), 530-536. DOI
11	S.S. Miller and P.T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Anal. Appl., 65 (1978), 282-305.
12	M. Nunokawa, On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad. Ser A, 69(7) (1993), 234-237. DOI
13	M. Nunokawa, On a certain of starlikeness, Math. Japonica, 44 (1996), 281-284.
14	M. Nunokawa, O.S. Kwon, Y.J. Sim and N.E. Cho, Sufficient conditions for Caratheodory functions, Filomat, 32(3) (2018), 1097-1106. DOI
15	M. Obradovic and S. Owa, A criterion for starlikeness, Math. Nachr., 140(1989), 97-102. DOI
16	R. Singh, On Bazilevc functions, Proc. Amer. Math. Soc., 38 (1973), 261-271.
17	S. Owa and M. Obradovic, Certain subclasses of Bazilevic functions of type α, Int. J. Math. Sci., 9 (1986), 347-359. DOI
18	K. Sakaguch, On a certain univalent mapping, J. Math. Soc. Japan, 11 (1959), 72-75. DOI
19	Y.J. Sim, O.S. Kwon, N.E. Cho and H.M. Srivastava, Some sets of sufficient conditions for Caratheodory functions. J. Comput. Anal. Appl., 21(7) (2016), 1243-1254.
20	K. Vijaya, G. Murugusundaramoorthy and N.E. Cho, Majorization problems for uniformly starlike functions based on Ruscheweyh q-differential operator related with exponential function, Nonlinear Funct. Anal. Appl., 26(1) (2021), 71-81. doi.org/10.22771/nfaa.2021.26.01.05 DOI
21	L.M. Wang, The tilted Caratheodory class and its applications, J. Kor. Math. Soc., 49(4) (2012), 671-686. doi:10.4134/JKMS.2012.49.4.671 DOI