Early Coefficient Bounds and Fekete–Szegö Inequality for a Subclass of Analytic Functions Defined by a New Generalized Differential Operator

In this paper, a new subclass, E_(ψ,κ,τ) (σ,λ,μ,α,β,δ,η,l,t) of analytic functions, defined through a new generalized differential operator D_(μ,λ,σ)^m (α,β,δ,η,l,t) and the Janowski function is introduced and analyzed. The subclass E_(ψ,κ,τ) (σ,λ,μ,α,β,δ,η,l,t), is constructed via subordination involving a linear combination of the operator and its derivatives. For this class, sharp bounds for the initial coefficients |a_2 | and |a_3 | were established and a precise form of the Fekete–Szegö inequality derived.

Univalent functions, generalized differential operator, Unit disc, Janowski Function

1. O. P. Ahuja, S. Kumar, and V. Ravichandran. Applications of first-order differential subordination for functions with positive real part. Studia Universitatis Babes-Bolyai Mathematica, 63(3):303–311, 2018. [Google Scholar] [Crossref]

2. F. M. Al-Oboudi. On univalent functions defined by a generalized salagean operator. International Journal of Mathematics and Mathematical Sciences, 27:1429–1436, 2004. [Google Scholar] [Crossref]

3. A. Amourah and F. Yousef. Some properties of a class of analytic functions involving a new generalized differential operator. Boletim da Sociedade Paranaense de Matemática, 38(6):33–42, 2020. [Google Scholar] [Crossref]

4. N. Bohra and V. Ravichandran. Schwarzian derivative and janowski convexity. Studia Universitatis Babes-Bolyai Mathematica, 62(2):165–174, 2017. [Google Scholar] [Crossref]

5. Carathéodory. Über den variabilitätsbereich der koeffizienten von potenzreihen, die gegebene werte nicht annehmen. Mathematische Annalen, 64:95–115, 1907. [Google Scholar] [Crossref]

6. M. Darus and R. W. Ibrahim. On subclasses for generalized operators of complex order. Far East Journal of Mathematical Sciences, 33(3):299–308, 2009. [Google Scholar] [Crossref]

7. T. He, S.-H. Li, L.-N. Ma, and H. Tang. Closure properties for second-order 𝜆-hadamard product of a class of meromorphic Janowski function. AIMS Mathematics, 8(5):12133–12142, 2023. [Google Scholar] [Crossref]

8. W. Janowski. Some extremal problems for certain families of analytic functions. Annales Polonici Mathematici, 28:297–326, 1973. [Google Scholar] [Crossref]

9. O. O. Opoola. On a subclass of univalent functions defined by a generalized differential operator. International Journal of Mathematical Analysis, 11(18):869–876, 2017. [Google Scholar] [Crossref]

10. E. A. Oyekan, I. T. Awolere, and O. A. Olukoya. Univalent function subclasses defined via a new extension of the Salagean operator. In Proceedings of the 3rd International Conference, American University of Nigeria, volume 3, pages 680–693, 2025. 11 [Google Scholar] [Crossref]

11. S. F. Ramadan and M. Darus. On the fekete–szegö inequality for a class of analytic functions defined by using generalized differential operator. Acta Universitatis Apulensis, 26:167–178, 2011. [Google Scholar] [Crossref]

12. M. Sharma, S. Kumar, and N. Jain. Differential subordination implications for certain carathéodory functions. Studia Universitatis Babes-Bolyai Mathematica, 68(4):1–15, 2023. [Google Scholar] [Crossref]

13. G. Singh and G. Singh. Certain subclasses of multivalent close-to-convex functions associated with generalized janowski functions. Sarajevo Journal of Mathematics, 21(1):1–20, 2024. [Google Scholar] [Crossref]

14. G. S. Sălăgean. Subclasses of univalent functions. pages 362–372, 1983. [Google Scholar] [Crossref]

15. S. R. Swamy. On univalent functions defined by a new generalized multiplier differential operator. Journal of Mathematical and Computational Science, 2(5):1233–1240, 2012. [Google Scholar] [Crossref]

16. M. Çağlar, Y. Polatoğlu, A. Şen, E. Yavuz, and S. Owa. On janowski starlike functions. Journal of Inequalities and Applications, 2007:1–14, 2008 [Google Scholar] [Crossref]

17. O. A. Olukoya (2026). On A Certain Subclass of Analytic Functions Defined Via a Generalized Differential Operator. , 13(3), https://doi.org/10.51244/IJRSI.2026.1303000045 [Google Scholar] [Crossref]

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