Class of Meromorphic Univalent Functions with Fixed Second Positive Coefficients Defined by q-Difference Operator: Class of Meromorphic Univalent Functions with Fixed Second Positive Coefficients

Zienab M.  Saleh; Adela O.  Mostafa

doi:10.53560/PPASA(59-1)640

Authors

Zienab M. Saleh Department of Mathematics, Faculty of Science, Mansoura University, Egypt
Adela O. Mostafa Department of Mathematics, Faculty of Science, Mansoura University, Egypt

DOI:

https://doi.org/10.53560/PPASA(59-1)640

Keywords:

Meromorphic, starlike, convex, fixed coefficient, radius of convexity

Abstract

In this paper using a q-difference operator, a class of meromorphic univalent functions with fixed second positive coefficients is defined. Coefficient estimates, some distortion theorems and other properties for this class are obtained. Various results obtained are sharp.

References

M. K. Aouf, On a certain class of meromorphic univalent functions with positive coefficients, Rend. Mat. Appl., 7 (11) (1991), no. 2, 209-219.

M. K. Aouf and H. E. Darwish, Certain meromorphically starlike functions with positive and fixed second coefficients, Tr. J. of Mathematics.,21 (1997), 311- 316.

M. K. Aouf and S. M. Madian, Inclusion and properties neighbourhood for certain p-valent functions associated with complex order and q–p-valent Cătaş operator, J. Sci. Taibah Univer. Sci., 14(1) (2020) , 1226-1232.

M. K. Aouf, A. O. Mostafa and F. Y. AL-Quhali, Properties for class of β- uniformly univalent functions defined by Sălăgean type q-difference operator, Int. J. Open Probl. Complex Anal., 11 (2019), no. 2, 1–16.

J. Clunie, On meromorpic schlicht functions, J. Lond. Math.Soc., 34 (1959), 215-216.

B. A. Frasin and M. Darus, On certain meromorphic functions with positive coefficients, Southeast Asian Bull. Math., 28 (2004), 615-623.

F. Ghanim and M. Darus, On certain subclass of meromorphic univalent functions with fixed residue, Far East J. Math. Sci. (FJMS)., 26 (2007), 195- 207.

F. Ghanim and M. Darus, A new subclass of uniformly starlike and convex functions with negative coefficients, Int. J. Pure Appl. Math., 45 (4) (2008), 559-572.

F. Ghanim and M. Darus, On a certain subclass of meromorphic univalent functions with fixed second positive coefficients, Surveys in Mathematics and its Applications., 5 (2010), 49-60.

R. M. Goel and N. S. Sohi, On a class of meromorphic functions, Glas. Mat., 3. Ser., 17 (37) (1982), 19-28.

A.W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc., 8 (1957), 598-601.

Jinxi Ma, Extreme points and minimal outer area problem for meromorphic univalent functions, J. Math. Anal. Appl., 220 (2) (1998), 769-773.

J. Miller, Convex meromorphic mappings and related functions, Proc. Am. Math. Soc., 25 (1970), 220-228.

St. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 81 (1981) 521- 527.

H. M. Srivastava and S. Owa, Current Topics In Analytic Functions Theory, World Scientific, Singapore, 1992.

H. Tang, H. M. Zayed, A. O. Mostafa and M. K. Aouf, Fekete-Szegö problems for certain classes of meromorphic functions using q-derivative operator, J. Math. Resear. Appl., 38 (2018), no. 3, 236-246.

B. A. Uralgaddi and M. D. Ganigi, A certain class of meromorphically starlike functions with positive coefficients, Pure Appl. Math. Sci., 26 (1987), 75- 81.

B. A. Uralegaddi and C. Somanatha, Certain differential operators for meromorphic functions, Houston J. Math., 17 (1991), 279-284.

B. A. Uralegaddi and C. Somanatha, New criteria for meromorphic starlike univalent functions, Bull. Austral. Math. Soc., 43 (1991), 137-140.

Class of Meromorphic Univalent Functions with Fixed Second Positive Coefficients Defined by q-Difference Operator