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Fuzzy Differential Subordination Associated with a General Linear Transformation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Sarfraz Nawaz Malik & Nazar Khan & Ferdous M. O. Tawfiq & Mohammad Faisal Khan & Qazi Zahoor Ahmad & Qin Xin, 2023. "Fuzzy Differential Subordination Associated with a General Linear Transformation," Mathematics, MDPI, vol. 11(22), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4582-:d:1276539
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    References listed on IDEAS

    as
    1. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Yang, Xuehua & Wu, Lijiao & Zhang, Haixiang, 2023. "A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    3. F. M. Al-Oboudi, 2004. "On univalent functions defined by a generalized Sălăgean operator," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-8, January.
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