Startseite Radius estimates for functions in the class 𝒰r(λ)
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Radius estimates for functions in the class 𝒰r(λ)

  • Baskar Babujee Janani EMAIL logo und Vaithiyanathan Ravichandran
Veröffentlicht/Copyright: 24. Oktober 2025
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

A normalized analytic function f defined on the open unit disc đ”» is called Ma-Minda starlike if the function zfâ€Č/f is subordinate to the function φ. For 0 < λ ≀ 1, let 𝒰(λ) denote the class of functions f(z)=z+∑n=2∞anzn analytic in the unit disc đ”» satisfying the condition |(z/f(z))2fâ€Č(z)−1| < λ for z ∈ đ”». The class 𝒰r(λ) consists of functions g defined by g(z) = ((z/f(z)) − 1)/(−a2), where f ∈ 𝒰(λ) and a2 = fâ€Čâ€Č(0)/2 ≠ 0. The radius of Janowski starlikeness and in particular, the radius of starlikeness of order Îł are derived. Also, the sharp radii of Ma-Minda starlikeness associated with nephroid, lune, lemniscate of Bernoulli, cardioid, rational function, and so on, are estimated. The inclusion conditions based on λ are derived as specific cases so that functions in the class 𝒰r(λ) are included in various Ma-Minda starlike classes.

MSC 2010: 30C80; 30C45

Acknowledgement

The authors thank the referees for their comments and valuable suggestions.

  1. (Communicated by StanisƂawa Kanas)

References

[1] Ali, R. M.—Alareefi, N. M.: The 𝒰-radius for classes of analytic functions, Bull. Malays. Math. Sci. Soc. 38(4) (2015), 1705–1721.Suche in Google Scholar

[2] Arora, K.—Kumar, S. S.: Starlike functions associated with a petal shaped domain, Bull. Korean Math. Soc. 59(4) (2022), 993–1010.Suche in Google Scholar

[3] 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(1) (2019), 213–232.Suche in Google Scholar

[4] Gandhi, S.: Radius estimates for three leaf function and convex combination of starlike functions. In: Mathematical analysis. I. Approximation theory, Springer Proc. Math. Stat., Vol. 306, Springer, Singapore, pp. 173–184.Suche in Google Scholar

[5] Gandhi, S.—Ravichandran, V.: Starlike functions associated with a lune, Asian-Eur. J. Math. 10(4) (2017), Art. 1750064.Suche in Google Scholar

[6] Goel, P.—Sivaprasad Kumar, S.: Certain class of starlike functions associated with modified sigmoid function, Bull. Malays. Math. Sci. Soc. 43(1) (2020), 957–991.Suche in Google Scholar

[7] Gupta, P.—Nagpal, S.—Ravichandran, V.: Inclusion relations and radius problems for a subclass of starlike functions, J. Korean Math. Soc. 58(5) (2021), 1147–1180.Suche in Google Scholar

[8] Kanas, S.—Wiƛniowska, A.: Conic regions and k-uniform convexity, J. Comput. Appl. Math. 1051–2 (1999), 327–336.Suche in Google Scholar

[9] Kanas, S.—Wiƛniowska, A.: Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl. 45(4) (2000), 647–657.Suche in Google Scholar

[10] Kanas, S.—Kamaljeet, G.: Radius of uniformly convex γ-spirallikeness of combination of derivatives of Bessel functions, Axioms 12(5) (2023), Art. 468.Suche in Google Scholar

[11] Kumar, S. S.—Kamaljeet, G.: A cardioid domain and starlike functions, Anal. Math. Phys. 11(2) (2021), Paper No. 54.Suche in Google Scholar

[12] Kumar, S.—Ravichandran, V.: A subclass of starlike functions associated with a rational function, Southeast Asian Bull. Math. 40(2) (2016), 199–212.Suche in Google Scholar

[13] Li, L.—Ponnusamy, S.—Wirths, K. J.: Relations of the class 𝒰(λ) to other families of functions, Bull. Malays. Math. Sci. Soc. 45(3) (2022), 955–972.Suche in Google Scholar

[14] Ma, W. C.—Minda, D.: A unified treatment of some special classes of univalent functions. In: Proceedings of the Conference on Complex Analysis (Tianjin, 1992), 157–169, Conf. Proc. Lecture Notes Anal., I, Int. Press, Cambridge, MA.Suche in Google Scholar

[15] Mendiratta, R.—Nagpal, S.—Ravichandran, V.: On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc. 38(1) (2015), 365–386.Suche in Google Scholar

[16] Mundalia, M.—Kumar, S. S.: On a subfamily of starlike functions related to hyperbolic cosine function, J. Anal. 31(3) (2023), 2043–2062.Suche in Google Scholar

[17] Obradović, M.—Ponnusamy, S.: Radius properties for subclasses of univalent functions, Analysis (Munich) 25(3) (2005), 183–188.Suche in Google Scholar

[18] Obradović, M.—Ponnusamy, S.—Wirths, K. J.: Geometric studies on the class 𝒰(λ), Bull. Malays. Math. Sci. Soc. 39(3) (2016), 1259–1284.Suche in Google Scholar

[19] Obradović, M.—Ponnusamy, S.—Wirths, K. J.: Logarithmic coefficients and a coefficient conjecture for univalent functions, Monatsh. Math. 185(3) (2018), 489–501.Suche in Google Scholar

[20] Obradović, M.—Tuneski, N.: Some properties of the class 𝒰, Ann. Univ. Mariae Curie-Sk lodowska Sect. A 73(1) (2019), 49–56.Suche in Google Scholar

[21] Obradović, M.—Ponnusamy, S.—Singh, V.—Vasundhra, P.: Univalency, starlikeness and convexity applied to certain classes of rational functions, Analysis (Munich) 22(3) (2002), 225–242.Suche in Google Scholar

[22] Obradović, M.—Pascu, N. N.—Radomir, I.: A class of univalent functions, Math. Japon. 44(3) (1996), 565–568.Suche in Google Scholar

[23] Ozaki, S.—Nunokawa, M.: The Schwarzian derivative and univalent functions, Proc. Amer. Math. Soc. 33 (1972), 392–394.Suche in Google Scholar

[24] Ponnusamy, S.—Wirths, K. J.: Coefficient problems on the class U(λ), Probl. Anal. Issues Anal. 7(25)(1) (2018), 87–103.Suche in Google Scholar

[25] Raina, R. K.—SokóƂ, J.: Some properties related to a certain class of starlike functions, C. R. Math. Acad. Sci. Paris 353(11) (2015), 973–978.Suche in Google Scholar

[26] Ravichandran, V.—Rþnning, F.—Shanmugam, T. N.: Radius of convexity and radius of starlikeness for some classes of analytic functions, Complex Variables Theory Appl. 33(1–4) (1997), 265–280.Suche in Google Scholar

[27] Rþnning, F.: Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118(1) (1993), 189–196.Suche in Google Scholar

[28] Sharma, K.—Jain, N. K.—Ravichandran, V.: Starlike functions associated with a cardioid, Afr. Mat. 27(5–6) (2016), 923–939.Suche in Google Scholar

[29] Shanmugam, T. N.—Ravichandran, V.: Certain properties of uniformly convex functions. In: Computational methods and function theory 1994 (Penang), 319–324, Ser. Approx. Decompos., 5, World Sci. Publ., River Edge, NJ.Suche in Google Scholar

[30] Silverman, H.—Silvia, E. M.: Subclasses of starlike functions subordinate to convex functions, Canad. J. Math. 37(1) (1985), 48–61.Suche in Google Scholar

[31] SokóƂ, J.—Stankiewicz, J.: Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat. No. 19 (1996), 101–105.Suche in Google Scholar

[32] Vasudevarao, A.—Yanagihara, H.: On the growth of analytic functions in the class 𝒰(λ), Comput. Methods Funct. Theory 13(4) (2013), 613–634.Suche in Google Scholar

[33] Wani, L. A.—Swaminathan, A.: Radius problems for functions associated with a nephroid domain, Rev. R. Acad. Cienc. Exactas Fı́s. Nat. Ser. A Mat. RACSAM 114(4) (2020), Paper No. 178.Suche in Google Scholar

[34] Wani, L. A.—Swaminathan, A.: Starlike and convex functions associated with a nephroid domain, Bull. Malays. Math. Sci. Soc. 44(1) (2021), 79–104.Suche in Google Scholar

Received: 2024-10-01
Accepted: 2025-07-02
Published Online: 2025-10-24
Published in Print: 2025-10-27

© 2025 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. Copies of monomorphic structures
  2. Endomorphism kernel property for extraspecial and special groups
  3. Sums of Tribonacci numbers close to powers of 2
  4. Multiplicative functions k-additive on hexagonal numbers
  5. Monogenic even cyclic sextic polynomials
  6. Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
  7. Degree of independence in non-archimedean fields
  8. Remarks on some one-ended groups
  9. Some new characterizations of weights for hardy-type inequalities with kernels on time scales
  10. Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
  11. Radius estimates for functions in the class 𝒰r(λ)
  12. Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
  13. More q-congruences from Singh’s quadratic transformation
  14. Stability and controllability of cycled dynamical systems
  15. Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
  16. Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
  17. Coincidence points via tri-simulation functions with an application in integral equations
  18. On Fong-Tsui conjecture and binormality of operators
  19. Riemannian maps of CR-submanifolds of Kaehler manifolds
  20. On structural numbers of topological spaces
  21. The Îș-FrĂ©chet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
  22. Weighted pseudo S-asymptotically (ω, c)-periodic solutions to fractional stochastic differential equations
Heruntergeladen am 26.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2025-0081/pdf
Button zum nach oben scrollen