Fuzzy Differential Subordination Associated with a General Linear Transformation

Sarfraz Nawaz Malik (), Nazar Khan (), Ferdous M. O. Tawfiq, Mohammad Faisal Khan, Qazi Zahoor Ahmad and Qin Xin
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Sarfraz Nawaz Malik: Department of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, Pakistan
Nazar Khan: Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan
Ferdous M. O. Tawfiq: Department of Mathematics, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
Mohammad Faisal Khan: Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia
Qazi Zahoor Ahmad: Department of Mathematics, Government Akhtar Nawaz Khan (Shaheed) Degree College KTS, Haripur 22620, Pakistan
Qin Xin: Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands

Mathematics, 2023, vol. 11, issue 22, 1-17

Abstract: 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 BS α , λ m , t : A n → A n in the open unit disc U . The second step is to develop fuzzy differential subordination for the operator BS α , λ m , t . By considering linear transformations of the operator BS α , λ m , t , we define a new fuzzy class of analytic functions in U which we denote by T ϝ λ , t ( m , α , δ ) . Several innovative results are found using the concept of fuzzy differential subordination and the operator BS α , λ m , t for the function f in the class T ϝ λ , 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: linear transformation; fuzzy differential subordination; fuzzy set; analytic functions; Al-Oboudi differential operator; Babalola convolution operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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