Title: On p-Valent Strongly Starlike and Strongly Convex Functions Associated with Generalized Linear Operator
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-20-00023; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 104-111
Document Type: Research Paper
aDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
bDepartment of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt. Current Address: Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah 51452, Saudi Arabia
Received: 11 August 2020, Accepted: 1 December 2020, Published: 25 April 2021.
Corresponding Author: Sheza M. El-Deeb (Email address: email@example.com)
Full Text: PDF
In this paper, we define some new subclasses and of strongly starlike and strongly convex functions of order and type by using the generalized linear operator . We also derive some interesting properties, such as inclusion relationships of these classes and the integral operator .
Keywords: Analytic functions, p-valent, Strongly starlike, Strongly convexReferences:
- F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Internat. J. Math. Math. Sci. 27, 1429-1436, 2004.
- M. K. Aouf, Some inclusion relationships associated with the Komatu integral operator, Math. Comput. Modelling 50, 1360-1366, 2009.
- M. K. Aouf, The Komatu integral operator and strongly close-to-convex functions, Bull. Math. Anal. Appl. 3 (3), 209-219, 2011.
- M . K. Aouf, R. M. El-Ashwah and S. M. El-Deeb, Some inequalities for certain p-valent functions involving an extended multiplier transformations, Proc. Pakistan Acad. Sci. 46 (4), 217-221, 2009.
- M. K. Aouf and H.M. Hossen, New criteria for meromorphic p -valent starlike functions, Tsukuba J. Math. 50 (17), 481-486, 1993.
- S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135, 429-446, 1969.
- J. H. Choi, M. Saigo and H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276, 432-445, 2002.
- A. Ebadian and S. Najafzadeh, Uniformly starlike and convex univalent functions by using certain integral operator, Acta Univ. Apulensis 20, 17-23, 2009.
- A. Ebadian, S. Shams, Z. G. Wang and Y. Sun, A class of multivalent analytic functions involving the generalized Jung-Kim-Srivastava operator, Acta Univ. Apulensis 18, 265-277, 2009.
- R. M. El-Ashwah, M . K. Aouf and S. M. El-Deeb, Differential subordination for certian subclasses of p-valent functions assoicated with generalized linear operator, J. Math. Art. ID692045, 1-8, 2013.
- A. W. Goodman, On the Schwarz Christoffel transformation and p-valent functions, Trans. Amer. Math. Soc. 68, 204-233, 1950.
- S. M. Khairnar and M. More, On a subclass of multivalent β-uniformly starlike and convex functions defined by a linear operator, IAENG Int. J. Appl. Math. 39 (3), 1-9, 2009.
- N. Khan, Q. Z. Ahmad, T. Khalid and B. Khan, Results on spirallike p-valent functions, AIMS Math. 1, 12-20, 2017.
- B. Khan, Z.-G. Liu, H. M. Srivastava, N. Khan, M. Darus and M. Tahir, A study of some families of multivalent q-starlike functions involving higher-order q-derivatives, Mathematics 8, Art. ID 1470, 1-12, 2020.
- Y. Komatu, On analytic prolongation of a family of integral operators, Math. (Cluj) 32 (55), 141-145, 1990.
- T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, New York, 1991.
- C. P. Lu, Prime submodules of modules, Comment. Math. Univ. St. Pauli 33 (1), 61-69, 1984.
- A. Muhammad, On p-valent strongly starlike and strongly convex functions, Acta Univ. Apulensis 26, 17-188, 2011.
- M. Nunokawa, On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad.Ser. A Math. Sci. 69 (7), 234-237, 1993.
- M. Nunokawa, S. Owa and A. Ikeda, On the strongly starlikeness of multivalently convex functions of order α, Hindawi Publishing Corp. 51-55, 2001.
- M. Nunokawa, S. Owa, H. Saitoh and A. Ikeda, Some results for strongly starlike functions, J. Math. Anal. Appl. 212, 98-106, 1997.
- M. Obradovic and S. B. Joshi, On certain classes of strongly starlike functions, Taiwan.J. Math. 2, 297-302, 1998.
- S. Owa, On certain classes of p-valent functions with negative coefficients, Bull. Belg. Math. Soc. Simon Stevin 59, 385-402, 1985.
- D. A. Patel and N. K. Thakare, On convex hulls and extreme points of p-valent starlike and convex classes with applications, Bull. Math. Soc. Sci. Math. Roumanie (N.S) 27, 145-160, 1983.
- J. K. Prajapat and S. P. Goyal, Applications of Srivastava-Attiya operator to the classes of strongly starlike and strongly convex functions, J. Math. Inequal. 3 (1), 129-137, 2009.
- R. K. Raina and I. B. Bapna, On the starlikeness and convexity of a certain integral operator, Southeast Asian Bull. Math. 33, 101-108, 2009.
- G. S. Salagean, Subclasses of univalent functions, Lecture Notes in Math. ( Springer-Verlag ) 1013, 362-372, 1983.
- S. Shams, S. R. Kulkarni and J. M. Jahangiri, Subordination properties for p-valent functions defined by integral operator, Internat. J. Math. Math. Sci. Art. ID94572, 1-3, 2006.
- H. M. Srivastava, Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iran. J. Sci. Technol. Trans. A: Sci. 44, 327-344, 2020.
- H. M. Srivastava, Q. Z. Ahmad, N. Khan, S. Kiran and B. Khan, Some applications of higher order derivatives involving certain subclasses of analytic and multivalent functions, J. Nonlinear Var. Anal. 2, 343-353, 2018.
- H. M. Srivastava, M. K. Aouf and A. O. Mostafa, Some properties of analytic functions associated with fractional q-calculus operators, Miskolc Math. Notes 20, 1245-1260, 2019.
- H. M. Srivastava and S. M. El-Deeb, A certain class of analytic functions of complex order connected with a q-analogue of integral operators, Miskolc Math. Notes 21, 417-433, 2020.