Analytic Functions Related to a Balloon-Shaped Domain

Adeel Ahmad, Jianhua Gong, Isra Al-Shbeil, Akhter Rasheed, Asad Ali, Saqib Hussain

Research output: Contribution to journalArticlepeer-review


One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new class of normalized analytic functions (Formula presented.) defined in the new domain, including the sharp estimates for the coefficients (Formula presented.), and (Formula presented.), and for three second-order and third-order Hankel determinants, (Formula presented.), and (Formula presented.). The optimality of each obtained estimate is given as well.

Original languageEnglish
Article number865
JournalFractal and Fractional
Issue number12
Publication statusPublished - Dec 2023


  • Hankel determinant
  • analytic function
  • generalized domain
  • sharp upper bound
  • subordination

ASJC Scopus subject areas

  • Analysis
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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