The GFT group is working on the following problems with the related papers in this direction listed as follows:
Reformulation of Miller and Mocanu's Differential Subordination Theory for Functions with Preassigned Initial Coefficient and its Applications
Gupta, Prachi; Nagpal, Sumit; Ravichandran, V. Marx-Strohhäcker theorem for multivalent functions. Afr. Mat. 32 (2021), no. 7-8, 1421--1434. MR4327479
Sharma, Kanika; Ravichandran, V. Applications of theory of differential subordination of functions with fixed initial coefficient. J. Class. Anal. 8 (2016), no. 2, 113--121. MR3535230
Mendiratta, Rajni; Nagpal, Sumit; Ravichandran, V. Second-order differential superordination for analytic functions with fixed initial coefficient. Southeast Asian Bull. Math. 39 (2015), no. 6, 851--864. MR3444396
Lee, See Keong; Ravichandran, V.; Supramaniam, Shamani. Applications of differential subordination for functions with fixed second coefficient to geometric function theory. Tamsui Oxf. J. Inf. Math. Sci. 29 (2013), no. 2, 267--284. MR3244168
Nagpal, Sumit; Ravichandran, V. Applications of the theory of differential subordination for functions with fixed initial coefficient to univalent functions. Ann. Polon. Math. 105 (2012), no. 3, 225--238. MR2950658
Ali, Rosihan M.; Nagpal, Sumit; Ravichandran, V. Second-order differential subordination for analytic functions with fixed initial coefficient. Bull. Malays. Math. Sci. Soc. (2) 34 (2011), no. 3, 611--629. MR2823592
Geometric Properties of Univalent Harmonic Mappings: Convolution Properties; Construction Techniques; Radius Problems
Raj, Ankur; Nagpal, Sumit. Stable close-to-convexity and radius of full convexity for sense-preserving harmonic mappings. Rocky Mountain J. Math. 54 (2024), no. 5, 525–540 . MR4743451
Raj, Ankur; Nagpal, Sumit. Radius of convexity for analytic part of sense-preserving harmonic mappings. Bull. Malays. Math. Sci. Soc. 45 (2022), no. 5, 2665--2679. MR4489583
Beig, Subzar; Ravichandran, Vaithiyanathan. Directional convexity of combinations of harmonic half-plane and strip mappings. Commun. Korean Math. Soc. 37 (2022), no. 1, 125--136. MR4415591
Raj, Ankur; Nagpal, Sumit; Ravichandran, V. On the product of planar harmonic mappings. Comput. Methods Funct. Theory 21 (2021), no. 3, 427--452. MR4299907
Beig, Subzar; Ravichandran, V. Convolution and convex combination of harmonic mappings. Bull. Iranian Math. Soc. 45 (2019), no. 5, 1467--1486. MR4020725
Ahuja, Om P.; Cetinkaya, Asena; Ravichandran, V. Harmonic univalent functions defined by post quantum calculus operators. Acta Univ. Sapientiae Math. 11 (2019), no. 1, 5--17. MR3995733
Ahuja, Om P.; Beig, Subzar; Ravichandran, V. Univalent harmonic functions generated by Ruscheweyh derivatives of analytic functions. Acta Univ. Apulensis Math. Inform. No. 59 (2019), 13--24. MR4024486
Beig, Subzar; Ravichandran, V. Directional convexity of harmonic mappings. Bull. Malays. Math. Sci. Soc. 41 (2018), no. 2, 1045--1060. MR3781557
Ahuja, Om P.; Nagpal, Sumit; Ravichandran, V. A technique of constructing planar harmonic mappings and their properties. Kodai Math. J. 40 (2017), no. 2, 278--288. MR3680562
Nagpal, Sumit; Ravichandran, V. Convolution properties of the harmonic Koebe function and its connection with 2-starlike mappings. Complex Var. Elliptic Equ. 60 (2015), no. 2, 191--210. MR3298078
Nagpal, Sumit; Ravichandran, V. Univalence and convexity in one direction of the convolution of harmonic mappings. Complex Var. Elliptic Equ. 59 (2014), no. 9, 1328--1341. MR3210304
Nagpal, Sumit; Ravichandran, V. A subclass of close-to-convex harmonic mappings. Complex Var. Elliptic Equ. 59 (2014), no. 2, 204--216. MR3170754
Nagpal, Sumit; Ravichandran, V. Starlikeness, convexity and close-to-convexity of harmonic mappings. Current topics in pure and computational complex analysis, 201--214, Trends Math., Birkhauser/Springer, New Delhi, 2014. MR3329718
Ahuja, Om P.; Nagpal, Sumit; Ravichandran, V. Radius constants for functions with the prescribed coefficient bounds. Abstr. Appl. Anal. 2014, Art. ID 454152, 12 pp. MR3261223
Nagpal, Sumit; Ravichandran, V. A comprehensive class of harmonic functions defined by convolution and its connection with integral transforms and hypergeometric functions. Stud. Univ. Babeş-Bolyai Math. 59 (2014), no. 1, 41--55. MR3197914
Nagpal, Sumit; Ravichandran, V. Fully starlike and fully convex harmonic mappings of order $\alpha$. Ann. Polon. Math. 108 (2013), no. 1, 85--107. MR3021270
Properties of Special Functions in connection with GFT
Naz, Adiba; Nagpal, Sumit; Ravichandran, V. Exponential radii of starlikeness and convexity of some special functions. Ramanujan J. 65 (2024), no. 1, 391–427. MR4789402
Naz, Adiba; Nagpal, Sumit; Ravichandran, V. Geometric properties of generalized Bessel function associated with the exponential function. Math. Slovaca 73 (2023), no. 6, 1459–1478. MR4678552
Naz, Adiba; Nagpal, Sumit; Ravichandran, V. Exponential starlikeness and convexity of confluent hypergeometric, Lommel, and Struve functions. Mediterr. J. Math. 17 (2020), no. 6, Paper No. 204, 22 pp. MR4172977
Madaan, Vibha; Kumar, Ajay; Ravichandran, V. Radii of starlikeness and convexity of some entire functions. Bull. Malays. Math. Sci. Soc. 43 (2020), no. 6, 4335--4359. MR4166143
Madaan, Vibha; Kumar, Ajay; Ravichandran, V. Lemniscate convexity of generalized Bessel functions. Studia Sci. Math. Hungar. 56 (2019), no. 4, 404--419. MR4048763
Bohra, Nisha; Ravichandran, V. Radii problems for normalized Bessel functions of first kind. Comput. Methods Funct. Theory 18 (2018), no. 1, 99--123. MR3764714
Bohra, N.; Ravichandran, V. On confluent hypergeometric functions and generalized Bessel functions. Anal. Math. 43 (2017), no. 4, 533--545. MR3738359
Ali, Rosihan M.; Mondal, Saiful R.; Ravichandran, V. On the Janowski convexity and starlikeness of the confluent hypergeometric function. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 2, 227--250. MR3351038
Nagpal, Sumit; Ravichandran, V. A comprehensive class of harmonic functions defined by convolution and its connection with integral transforms and hypergeometric functions. Stud. Univ. Babeş-Bolyai Math. 59 (2014), no. 1, 41--55. MR3197914
Problems associated with Bohr's Radius
Anand, Swati; Jain, Naveen Kumar; Kumar, Sushil. Sharp Bohr radius constants for certain analytic functions. Bull. Malays. Math. Sci. Soc. 44 (2021), no. 3, 1771--1785. MR4241333
Jain, Naveen Kumar; Yadav, Shalu. Bohr radius for certain analytic functions. Mathematical analysis. I. Approximation theory, 211--221, Springer Proc. Math. Stat., 306, Springer, Singapore, [2020]. MR4099177
Ali, Rosihan M.; Jain, Naveen Kumar; Ravichandran, Vaithiyanathan. Bohr radius for classes of analytic functions. Results Math. 74 (2019), no. 4, Paper No. 179, 13 pp. MR4025539
Radius Problems by Fixing Second Coefficient
Anand, Swati; Jain, Naveen Kumar; Kumar, Sushil. Normalized analytic functions with fixed second coefficient. J. Anal. 31 (2023), no. 3, 1917–1938. MR4620979
Ravichandran, V.; Nagpal, Sumit. A survey on univalent functions with fixed second coefficient. Math. Newsl. 33 (2022), no. 1, 17--28. MR4518875
Ali, Rosihan M.; Kumar, Virendra; Ravichandran, V.; Sivaprasad Kumar, Shanmugam. Radius of starlikeness for analytic functions with fixed second coefficient. Kyungpook Math. J. 57 (2017), no. 3, 473--492. MR3722703
Mendiratta, Rajni; Nagpal, Sumit; Ravichandran, V. Radii of starlikeness and convexity for analytic functions with fixed second coefficient satisfying certain coefficient inequalities. Kyungpook Math. J. 55 (2015), no. 2, 395--410. MR3367954
Ali, Rosihan M.; Cho, Nak Eun; Jain, Naveen Kumar; Ravichandran, V. Radii of starlikeness and convexity for functions with fixed second coefficient defined by subordination. Filomat 26 (2012), no. 3, 553--561. MR3098260
Problems associated with Schwarzian Derivatives
Sebastian, Asha; Ravichandran, V. Criteria for starlikeness using schwarzian derivatives. J. Anal. 32 (2024), no. 4, 1973–1990. MR4778966
Malik, Somya; Ravichandran, V. Schwarzian derivative and convexity of order $\alpha$. J. Anal. 31 (2023), no. 1, 201----228. MR4554000
Bohra, Nisha; Ravichandran, V. Schwarzian derivative and Janowski convexity. Stud. Univ. Babeş-Bolyai Math. 62 (2017), no. 2, 197--204. MR3660536
Ali, Rosihan M.; Ravichandran, V.; Seenivasagan, N. Subordination and superordination on Schwarzian derivatives. J. Inequal. Appl. 2008, Art. ID 712328, 18 pp. MR2470182
Toeplitz and Hankel Determinants
Kumar, Sushil; Pandey, Rakesh Kumar; Rai, Pratima. Certain sharp estimates of Ozaki close-to-convex functions. Asian-Eur. J. Math. 17 (2024), no. 6, Paper No. 2450047, 15 pp. MR4770532
Ali, Rosihan M.; Kumar, Sushil; Ravichandran, Vaithiyanathan. The third Hermitian-Toeplitz and Hankel determinants for parabolic starlike functions. Bull. Korean Math. Soc. 60 (2023), no. 2, 281--291. MR4569312
Kumar, Sushil; Rai, Pratima; Cetinkaya, Asena. Bound on Hankel determinants $H^{(2)}_4(f)$ and $H^{(3)}_4(f)$ for lemniscate starlike functions. Honam Math. J. 45 (2023), no. 1, 92--108. MR4548232
Kumar, Sushil; Kumar, Virendra. Sharp estimates on the third order Hermitian-Toeplitz determinant for Sakaguchi classes. Commun. Korean Math. Soc. 37 (2022), no. 4, 1041--1053. MR4505561
Ahuja, Om P.; Khatter, Kanika; Ravichandran, Vaithiyanathan. Toeplitz determinants associated with Ma-Minda classes of starlike and convex functions. Iran. J. Sci. Technol. Trans. A Sci. 45 (2021), no. 6, 2021--2027. MR4329220
Srivastava, H. M.; Kumar, Sushil; Kumar, Virendra; Cho, Nak Eun. Hermitian-Toeplitz and Hankel determinants for starlike functions associated with a rational function. J. Nonlinear Convex Anal. 23 (2022), no. 12, 2815--2833. MR4524975
Cho, Nak Eun; Kumar, Sushil; Kumar, Virendra. Hermitian-Toeplitz and Hankel determinants for certain starlike functions. Asian-Eur. J. Math. 15 (2022), no. 3, Paper No. 2250042, 16 pp. MR4404194
Ahuja, Om P.; Khatter, Kanika; Ravichandran, V. Symmetric Toeplitz determinants associated with a linear combination of some geometric expressions. Honam Math. J. 43 (2021), no. 3, 465--481. MR4331706
Kumar, Virendra; Kumar, Sushil. Bounds on Hermitian-Toeplitz and Hankel determinants for strongly starlike functions. Bol. Soc. Mat. Mex. (3) 27 (2021), no. 2, Paper No. 55, 16 pp. MR4266686
Khatter, Kanika; Ravichandran, V.; Sivaprasad Kumar, S. Third Hankel determinant of starlike and convex functions. J. Anal. 28 (2020), no. 1, 45--56. MR4077300
Kumar, Virendra; Kumar, Sushil; Ravichandran, V. Third Hankel determinant for certain classes of analytic functions. Mathematical analysis. I. Approximation theory, 223--231, Springer Proc. Math. Stat., 306, Springer, Singapore, [2020], 2020. MR4099178
Alarifi, Najla M.; Ali, Rosihan M.; Ravichandran, V. On the second Hankel determinant for the $k$th-root transform of analytic functions. Filomat 31 (2017), no. 2, 227--245. MR3628835
Lee, See Keong; Ravichandran, V.; Supramaniam, Shamani. Bounds for the second Hankel determinant of certain univalent functions. J. Inequal. Appl. 2013, 2013:281, 17 pp. MR3073988
Introduction and Study of classes of Ma-Minda type starlike functions
Anand, Swati; Rai, Pratima; Kumar, Sushil. Close-to-convex functions associated with a rational function. Math. Slovaca 74 (2024), no. 2, 339–354. MR4749967
Ahuja, Om P.; Çetinkaya, Asena; Kumar, Sushil. Geometric properties of starlikeness involving hyperbolic cosine function. Commun. Korean Math. Soc. 39 (2024), no. 2, 407–420. MR4739852
Gandhi, Shweta; Gupta, Prachi; Nagpal, Sumit; Ravichandran, V. Starlike functions associated with an epicycloid. Hacet. J. Math. Stat. 51 (2022), no. 6, 1637--1660. MR4510346
Gupta, Prachi; Nagpal, Sumit; Ravichandran, Vaithiyanathan. Inclusion relations and radius problems for a subclass of starlike functions. J. Korean Math. Soc. 58 (2021), no. 5, 1147--1180. MR4303808
Cho, N. E.; Kumar, V.; Kumar, S. S.; Ravichandran, V. Radius problems for starlike functions associated with the sine function. Bull. Iranian Math. Soc. 45 (2019), no. 1, 213--232. MR3913990
Kumar, Virendra; Cho, Nak Eun; Ravichandran, V.; Srivastava, H. M. Sharp coefficient bounds for starlike functions associated with the Bell numbers. Math. Slovaca 69 (2019), no. 5, 1053--1064. MR4017390
Khatter, Kanika; Ravichandran, V.; Sivaprasad Kumar, S. Starlike functions associated with exponential function and the lemniscate of Bernoulli. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), no. 1, 233--253. MR3902942
Gandhi, Shweta; Ravichandran, V. Starlike functions associated with a lune. Asian-Eur. J. Math. 10 (2017), no. 4, 1750064, 12 pp. MR3718233
Sharma, Kanika; Jain, Naveen Kumar; Ravichandran, V. Starlike functions associated with a cardioid. Afr. Mat. 27 (2016), no. 5-6, 923--939. MR3536076
Kumar, Sushil; Ravichandran, V. A subclass of starlike functions associated with a rational function. Southeast Asian Bull. Math. 40 (2016), no. 2, 199--212. MR3496681
Mendiratta, Rajni; Nagpal, Sumit; Ravichandran, V. On a subclass of strongly starlike functions associated with exponential function. Bull. Malays. Math. Sci. Soc. 38 (2015), no. 1, 365--386. MR3394060
Mendiratta, Rajni; Nagpal, Sumit; Ravichandran, V. A subclass of starlike functions associated with left-half of the lemniscate of Bernoulli. Internat. J. Math. 25 (2014), no. 9, 1450090, 17 pp. MR3266533
Radius Problems
Kaur, Gurpreet; Nagpal, Sumit. Radius problems for ratios of analytic functions involving sigmoid domain. Asian-Eur. J. Math. 17 (2024), no. 1, Paper No. 2350239, 16 pp. MR4706210
Kaur, Gurpreet; Nagpal, Sumit. Radius of convexity of classes associated with the ratio of derivative functions. Rend. Circ. Mat. Palermo (2) 73 (2024), no. 2, 587–601. MR4709079
Krishnan, Priya G.; Vaithiyanathan, Ravichandran; Saikrishnan, Ponnaiah. Radius problem associated with certain ratios and linear combinations of analytic functions. Math. Slovaca 74 (2024), no. 4, 877–894. MR4785238
Sharma, Meghna; Jain, Naveen Kumar; Kumar, Sushil. Starlikeness of analytic functions using special functions and subordination. Bol. Soc. Mat. Mex. (3) 30 (2024), no. 2, Paper No. 55, 19 pp. MR4751712
Krishnan, Priya G.; Ravichandran, V.; Saikrishnan, P. Radius of Ma-Minda starlikeness of certain normalised analytic functions. Filomat 37 (2023), no. 13, 4125–4153. MR4576571
Sebastian, Asha; Ravichandran, Vaithiyanathan. Radius of starlikeness through subordination. Stud. Univ. Babeş-Bolyai Math. 68 (2023), no. 1, 161--170. MR4568286
Malik, Somya; Ravichandran, V. Starlikeness of a product of starlike functions with non-vanishing polynomials. Anal. Math. Phys. 13 (2023), no. 2, Paper No. 28. MR4560555
Malik, Somya; Ali, Rosihan M.; Ravichandran, V. The Booth lemniscate starlikeness radius for Janowski starlike functions. Bull. Malays. Math. Sci. Soc. 45 (2022), no. 5, 2715--2732. MR4489586
Naz, Adiba; Kumar, Sushil; Ravichandran, V. Coefficient functionals and radius problems of certain starlike functions. Asian-Eur. J. Math. 15 (2022), no. 5, Paper No. 2250089, 19 pp. MR4429683
Yadav, Shalu; Sharma, Kanika; Ravichandran, V. Radius of starlikeness for some classes containing non-univalent functions. Asian-Eur. J. Math. 15 (2022), no. 1, Paper No. 2250009, 15 pp. MR4366394
Kanaga, R.; Ravichandran, V. Radius of Limaçon starlikeness for Janowski starlike functions. Asian-Eur. J. Math. 15 (2022), no. 9, Paper No. 2250164, 13 pp. MR4478088
Ahmad El-Faqeer, Ahmad Sulaiman; Haji Mohd, Maisarah; Supramaniam, Shamani; Ravichandran, Vaithiyanathan. Radius of starlikeness of functions defined by ratios of analytic functions. Appl. Math. E-Notes 22 (2022), 516--528. MR4496256
Madhumitha, S.; Ravichandran, V. Radius of starlikeness of certain analytic functions. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 115 (2021), no. 4, Paper No. 184, 18 pp. MR4311694
Sebastian, Asha; Ravichandran, V. Radius of starlikeness of certain analytic functions. Math. Slovaca 71 (2021), no. 1, 83--104. MR4216806
Lee, See Keong; Khatter, Kanika; Ravichandran, V. Radius of starlikeness for classes of analytic functions. Bull. Malays. Math. Sci. Soc. 43 (2020), no. 6, 4469--4493. MR4166151
Cho, Nak Eun; Kumar, Sushil; Kumar, Virendra; Ravichandran, V. Convolution and radius problems of analytic functions associated with the tilted Caratheodory functions. Math. Commun. 24 (2019), no. 2, 165--179. MR3984508
Cho, Nak Eun; Kumar, Sushil; Kumar, Virendra; Ravichandran, V. Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate. Turkish J. Math. 42 (2018), no. 3, 1380--1399. MR3804996
Verma, Shelly; Ravichandran, V. Radius problems for ratios of Janowski starlike functions with their derivatives. Bull. Malays. Math. Sci. Soc. 40 (2017), no. 2, 819--840. MR3620283
Jain, Naveen Kumar; Ravichandran, V. Product and convolution of certain univalent functions. Honam Math. J. 38 (2016), no. 4, 701--724. MR3700169
Ahuja, Om P.; Nagpal, Sumit; Ravichandran, V. Radius constants for functions with the prescribed coefficient bounds. Abstr. Appl. Anal. 2014, Art. ID 454152, 12 pp. MR3261223
Ali, Rosihan M.; Jain, Naveen Kumar; Ravichandran, V. On the radius constants for classes of analytic functions. Bull. Malays. Math. Sci. Soc. (2) 36 (2013), no. 1, 23--38. MR2989285
Kumar, Sushil; Rai, Pratima; Çetinkaya, Asena. Radius estimates of certain analytic functions. Honam Math. J. 43 (2021), no. 4, 627--639. MR4345176
Meromorphic Functions
Janani, B. B.; Ravichandran, V. Sufficient conditions for functions to be meromorphic starlike of reciprocal order $\alpha$. J. Anal. 32 (2024), no. 4, 2265–2280. MR4778982
Madhumitha, S.; Ravichandran, V. Differential subordination for analytic and meromorphic multivalent functions. Asian-Eur. J. Math. 16 (2023), no. 7, Paper No. 2350124, 15 pp. MR4613484