A note on generalized subclasses of multivalent quasi-convex functions

G. Singh; G. Singh

doi:10.2478/jamsi-2022-0007

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A note on generalized subclasses of multivalent quasi-convex functions

Journal of Applied Mathematics, Statistics and Informatics

Volume 18 (2022): Issue 1 (May 2022)

By: G. Singh and G. Singh

Open Access

|Jul 2022

Abstract

This paper is concerned with certain generalized subclasses of multivalent quasi-convex functions defined with subordination. Various properties of these classes in regard to the coefficient estimates, distortion theorems, growth theorems, argument theorems and inclusion relations are discussed. Also, the relations with the earlier known results are established.

References

H. R. Abdel-Gawad and D. K. Thomas, A subclass of close-to-convex functions, Publ. Inst. Math. (N. S.), 49(63)(1991), 61-66.
Search in Google Scholar Back to article
M. K. Aouf, On a class of p-valent starlike functions of order α, Int. J. Math. Math. Sci., 10(4)(1987), 733-744.10.1155/S0161171287000838
Search in Google Scholar Back to article
M. K. Aouf, On a class of p-valent close-to-convex functions of order β and type α, Int. J. Math. Math. Sci., 11(2)(1988), 259-266.10.1155/S0161171288000316
Search in Google Scholar Back to article
M. K. Aouf, On subclasses of p-valent close-to-convex functions, Tamkang J. Math., 22(2)(1991), 133-143.10.5556/j.tkjm.22.1991.4586
Search in Google Scholar Back to article
R. M. Goel and B. S. Mehrok, On a class of close-to-convex functions, Ind. J. Pure Appl. Math., 12(5)(1981), 648-658.
Search in Google Scholar Back to article
E. G. Goluzina, On the coefficients of a class of functions, regular in a disk having an integral representation in it, J. Soviet Math., 2(6)(1974), 606-617.10.1007/BF01089939
Search in Google Scholar Back to article
T. Hayami and S. Owa, The Fekete-Szegö problem for p-valently Janowski starlike and convex functions, Int. J. Math. Math. Sci., (2011), Article Id. 583972.10.1155/2011/583972
Search in Google Scholar Back to article
W. Janowski, Some extremal problems for certain families of analytic functions, Ann. Pol. Math., 28(1973), 297-326.10.4064/ap-28-3-297-326
Search in Google Scholar Back to article
W. Kaplan, Close-to-convex schlicht functions, Mich. Math. J., 1(1952), 169-185.10.1307/mmj/1028988895
Search in Google Scholar Back to article
S. R. Keogh and E. P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20(1969), 8-12.10.1090/S0002-9939-1969-0232926-9
Search in Google Scholar Back to article
J. Krzyz, On the derivative of close-to-convex functions, Colloq Math., 10(1963), 139-142.10.4064/cm-10-1-143-146
Search in Google Scholar Back to article
R. J. Libera, Some radius of convexity problems, Duke Math. J., 31(1964), 143-158.10.1215/S0012-7094-64-03114-X
Search in Google Scholar Back to article
M. S. Liu, On a subclass of p-valent close-to-convex functions of order β and type α, J. Math. Study, 30(1997), 102-104.
Search in Google Scholar Back to article
B. S. Mehrok, A subclass of close-to-convex functions, Bull. Inst. Math. Acad. Sin., 10(4)(1982), 389-398.
Search in Google Scholar Back to article
B. S. Mehrok and G. Singh, A subclass of close-to-convex functions, Int. J. Math. Anal., 4(27)(2010), 1319-1327.
Search in Google Scholar Back to article
Z. Nehari, Conformal Mappings, Mc. Graw Hill, New York, 1952.
Search in Google Scholar Back to article
K.I. Noor, On quasi-convex functions and related topics, Int. J. Math. Math. Sci., 10(1987), 241-258.10.1155/S0161171287000310
Search in Google Scholar Back to article
S. Ogawa, A note on close-to-convex functions, J. Nara Gakugei Univ., 8(1959), 9-10.
Search in Google Scholar Back to article
Y. Polatoglu, M. Bolkal, A. Sen and E. Yavuz, A study on the generalization of Janowski function in the unit disc, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 22(2006), 27-31.
Search in Google Scholar Back to article
M. O. Reade, On close-to-convex univalent functions, Michigan Math. J., 3(1955-56), 59-62.10.1307/mmj/1031710535
Search in Google Scholar Back to article
M. S. Robertson, On the theory of univalent functions, Ann. Math., 37(1936), 169-185.10.2307/1968451
Search in Google Scholar Back to article
St. Ruscheweyh and T. Sheil-Small, Hadamard product of schlicht functions and the Polya-Schoenberg conjecture, Comment. Math. Helv. 48(1973), 119-135.10.1007/BF02566116
Search in Google Scholar Back to article
C. Selvaraj and S. Stelin, On a generalized class of quasi-convex functions, Int. J. Pure Appl. Math., 101(6)(2015), 1051-1061.
Search in Google Scholar Back to article
C. Selvaraj, S. Stelin and S. Logu, On a subclass of close-to-convex functions associated with fixed second coefficient, Appl. Comput. Math., 4(5)(2015), 342-345.10.11648/j.acm.20150405.12
Search in Google Scholar Back to article
H. Singh and B. S. Mehrok, Subclasses of close-to-convex functions, Tamkang J. Math., 44(4)(2013), 377-386.10.5556/j.tkjm.44.2013.1080
Search in Google Scholar Back to article
G. Singh and G. Singh, Generalized subclasses of quasi-convex functions defined with subordination, Elec. J. Math. Anal. Appl., 9(2)(2021), 172-185.10.5817/AM2022-2-105
Search in Google Scholar Back to article
T. Umezawa, Multivalently close-to-convex functions, Proc. Amer. Math. Soc., 8(1957), 869-874.10.1090/S0002-9939-1957-0090654-9
Search in Google Scholar Back to article
L. Xiong and X. Liu, A general subclass of close-to-convex functions, Kragujevac J. Math., 36(2)(2012), 251-260.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/jamsi-2022-0007 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180

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Language: English

Page range: 93 - 107

Published on: Jul 4, 2022

Published by: University of Ss. Cyril and Methodius in Trnava

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Univalent functions,

Subordination,

multivalent functions,

close-to-convex functions,

quasi-convex functions,

General Terms: Regression,

Generalized linear model,

Related subjects:

Information technology,

Mathematics,

Logic and set theory,

Probability and statistics,

Applied mathematics

© 2022 G. Singh, G. Singh, published by University of Ss. Cyril and Methodius in Trnava
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 18 (2022): Issue 1 (May 2022)