Volume 21, Issue 1 (4-2026)
IJMSI 2026, 21(1): 1-11 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Bukhari S Z H, Tang H, Manzoor F. A Study of Some Geometric Aspects of a Subclass of Analytic Functions. IJMSI 2026; 21 (1) :1-11
URL: http://ijmsi.ir/article-1-2159-en.html
URL: http://ijmsi.ir/article-1-2159-en.html
Abstract:
We introduce a subclass k - T US∗(α, ϑ)of uniformly starlike functions fand study characterization theorem and coefficients estimates. We also define a neighbourhood of a function funder certain assumptions and study this neighborhood related results. We establish results relating to the partial sums of functions belonging to the class k - T US∗(α, ϑ). These functions are closely linked with the conformal mappings which lead to the growing applications in boundary and eigen-value problems in mathematics and various other fields of science and engineering. This research may also be related with the various
known classes already found in the literature.
known classes already found in the literature.
Type of Study: Research paper |
Subject:
Special
References
1. S. Z. H. Bukhari, M. Nazir, M. Raza, Some Generalizations of Analytic Functions with Respect to 2k-Symmetric Conjugate Points, Maejo Int. J. Sci. Technol., 10(01), (2016), 1-12. [DOI:10.15672/HJMS.20164512489]
2. S. Z. H. Bukhari, M. Raza, M. Nazir, Some Generalizations of the Class of Analytic Functions with Respect to k-Symmetric Points, Hacet. J. Math. Stat., 45(1), (2016), 1-14. [DOI:10.15672/HJMS.20164512489]
3. S. Z. H. Bukhari, T. Bulboac˘a, M. S. Shabbir, Subordination and Superordination Results for Analytic Functions with Respect to Symmetrical Points, Quaest. Math., 41(1), (2018), 1-15. [DOI:10.2989/16073606.2017.1372528]
4. A. W. Goodman, On Uniformly Convex Functions, Ann. Polon. Math., 56, (1991), 87-92. [DOI:10.4064/ap-56-1-87-92]
5. A. W. Goodman, On Uniformly Starlike Functions, J. Math. Anal. Appl., 155, (1991), 364-370. [DOI:10.1016/0022-247X(91)90006-L]
6. A. W. Goodman, Univalent Functions, Vol. I, Polygonal Publishing Washington, New Jersey, 1983.
7. A. W. Goodman, Univalent Functions and Analytic Curves, Proc. Amer. Math. Soc., 8(3), (1957), 598-601. [DOI:10.1090/S0002-9939-1957-0086879-9]
8. S. Kanas, Coefficient Estimates in Subclasses of the Caratheodory Class Related to Conical Domains, Acta Math. Univ. Comenian., 74(2), (2005), 149-161.
9. S. Kanas, H. M. Srivastava, Linear Operators Associated with k-Uniformly Convex Functions, Integral Transforms Spec. Funct., 9(2), (2000), 121-132. [DOI:10.1080/10652460008819249]
10. S. Kanas, A. Wi'sniowska, Conic Domains and Starlike Functions, Rev. Roumaine Math. Pures Appl., 45, (2000), 647-657.
11. S. Kanas and A. Wi'sniowska, Conic Regions and k-Uniform Convexity, J. Appl. Math., 105, (1999), 327-336. [DOI:10.1016/S0377-0427(99)00018-7]
12. H. A. Al-Kharsani, A. Sofo, Subordination Results on Harmonic k-Uniformly Convex Mappings and Related Classes, Comput. Math. Appl., 59(12), (2010), 3718-3726. [DOI:10.1016/j.camwa.2010.03.071]
13. A. Y. Lashin, On a Certain Subclass of Starlike Functions with Negative Coefficients, J. Ineq. Pure Appl. Math., 110(2), (2009), 1-18.
14. J. L. Li, S. Owa, Sufficient Conditions for Starlikeness, Indian J. Pure Appl. Math., 33, (2002), 313-318.
15. J. E. Littlewood, On Inequalities in the Theory of Functions, Proc. London Math. Soc., 23, (1925), 481-519. [DOI:10.1112/plms/s2-23.1.481]
16. W. C. Ma, D. Minda, Uniformly Convex Functions, Ann. Polon. Math., 57, (1992), 165-175. [DOI:10.4064/ap-57-2-165-175]
17. T. H. Macgregor, The Radius for Starlike Functions of Order 1/2 , Proc. Amer. Math. Soc., 14, (1963), 71-76. [DOI:10.1090/S0002-9939-1963-0150282-6]
18. S. Mahmood, I. Khan, S. N. Malik, S. Z. H. Bukhari, On Subclass of Alpha-Quasi Convex Functions Associated with Conic Regions, J. Inequa. special Funct., 7(4), (2017), 1-10. [DOI:10.1186/s13660-017-1535-4]
19. S. Mahmood, H. M. Srivastava, S. N. Malik, Some Subclasses of Uniformly Univalent Functions with Respect to Symmetric Points, Symmetry 11, (2019), Article ID 287, 1-14 [DOI:10.3390/sym11020287]
20. M. Obradovic, S. B. Joshi, On Certain Classes of Strongly Starlike Functions, Taiwanese J. Math., 2(3), (1998), 297-302. [DOI:10.11650/twjm/1500406969]
21. K. S. Padmanabhan, On Sufficient Conditions for Starlikeness, Indian J. Pure Appl. Math., 32(4), (2001), 543-550.
22. B. Pinchuk, On Starlike and Convex Functions of Order α, Duke Math. J., 35, (1968), 89-103. [DOI:10.1215/S0012-7094-68-03575-8]
23. M. S. Robertson, On the Theory of Univalent Functions, Ann. Math., 37, (1936), 374-408. [DOI:10.2307/1968451]
24. F. Ronning, On Starlike Functions Associated with Parabolic Regions, Ann. Univ. Mariae Curie-Sklodowska, Sect. A., 45, (1991), 117-122.
25. F. Ronning, Uniformly Convex Functions and a Corresponding Class of Starlike Functions, Proc. Amer. Math. Soc., 118, (1993), 189-196. [DOI:10.1090/S0002-9939-1993-1128729-7]
26. S. Ruscheweyh, Neighborhoods of Univalent Functions, Proc. Amer. Math. Soc., 81(4), (1981), 521-527. [DOI:10.1090/S0002-9939-1981-0601721-6]
27. A. Schild, On Starlike Functions of Order α, Amer. J. Math., 87, (1965), 65-70. [DOI:10.2307/2373224]
28. C. Selvarag, A. Selvakumaran, New Classes of k-Uniformly Convex and Starlike Functions with Respect to Other Points, Acta Math., 78(1), (2009), 103-114.
29. H. Silverman, A Survey with Open Problems on Univalent Functions Whose Coefficients are Negative, Rocky Mountain J. Math., 21(3), (1991), 1099-1125. [DOI:10.1216/rmjm/1181072932]
30. H. Silverman, Integral Means for Univalent Functions with Negative Coefficients, Houston J. Math., 23(1), (1997), 169-174.
31. H. Silverman, Partial Sums of Starlike and Convex Functions, J. Math. Anal. Appl., 209, (1997), 221-227. [DOI:10.1006/jmaa.1997.5361]
32. H. Silverman, Univalent Functions with Negative Coefficients, Proc. Amer. Math. Soc., 51, (1975), 109-116. [DOI:10.1090/S0002-9939-1975-0369678-0]
33. S. Singh, S. Gupta, First Order Differential Subordinations and Starlikeness of Analytic Maps in the Unit Disc, Kyungpook Math. J., 45, (2005), 395-404.
34. 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 Sci., 44, (2020), 327-344. [DOI:10.1007/s40995-019-00815-0]
35. H. M. Srivastava, Some Parametric and Argument Variations of the Operators of Fractional Calculus and Related Special Functions and Integral Transformations, J. Nonlinear Convex Anal., 22, (2021), 1501-1520.
36. H. M. Srivastava, S. Z. H. Bukhari, M. Nazir, A Subclass of α-Convex Functions with Respect to (2j, k)-Symmetric Conjugate Points, Bull. Iran. Math. Soc., 44, (2018), 1227-1242. [DOI:10.1007/s41980-018-0086-x]
37. H. M. Srivastava, G. Murugusundaramoorthy, T. Janani, Uniformly Starlike Functions and Uniformly Convex Functions Associated with the Struve Function, Internat. J. Appl. Math. Engrg. Sci., 8(2), (2014), 111-120. [DOI:10.4172/2168-9679.1000180]
38. H. M. Srivastava, S-H. Li, H. Tang, Certain Classes of k-Uniformly Close-to-Convex Functions and Other Related Functions Defined by Using the Dziok-Srivastava Operator, Bull. Math. Anal. Appl.,1(3), (2009), 49-63.
39. N. Xu, D. Yang, Some Criteria for Starlikeness and Strongly Starlikeness, Bull. Korean Math. Soc., 42(3), (2005), 579-590. [DOI:10.4134/BKMS.2005.42.3.579]
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
