Mathematics (Nov 2023)

Fuzzy Differential Subordination Associated with a General Linear Transformation

  • Sarfraz Nawaz Malik,
  • Nazar Khan,
  • Ferdous M. O. Tawfiq,
  • Mohammad Faisal Khan,
  • Qazi Zahoor Ahmad,
  • Qin Xin

DOI
https://doi.org/10.3390/math11224582
Journal volume & issue
Vol. 11, no. 22
p. 4582

Abstract

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In this study, we investigate a possible relationship between fuzzy differential subordination and the theory of geometric functions. First, using the Al-Oboudi differential operator and the Babalola convolution operator, we establish the new operator BSα,λm,t:An→An in the open unit disc U. The second step is to develop fuzzy differential subordination for the operator BSα,λm,t. By considering linear transformations of the operator BSα,λm,t, we define a new fuzzy class of analytic functions in U which we denote by Tϝλ,t(m,α,δ). Several innovative results are found using the concept of fuzzy differential subordination and the operator BSα,λm,t for the function f in the class Tϝλ,t(m,α,δ). In addition, we explore a number of examples and corollaries to illustrate the implications of our key findings. Finally, we highlight several established results to demonstrate the connections between our work and existing studies.

Keywords