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Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator

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  • Georgia Irina Oros

    (Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania)

Abstract

This paper is related to notions adapted from fuzzy set theory to the field of complex analysis, namely fuzzy differential subordinations. Using the ideas specific to geometric function theory from the field of complex analysis, fuzzy differential subordination results are obtained using a new integral operator introduced in this paper using the well-known confluent hypergeometric function, also known as the Kummer hypergeometric function. The new hypergeometric integral operator is defined by choosing particular parameters, having as inspiration the operator studied by Miller, Mocanu and Reade in 1978. Theorems are stated and proved, which give corollary conditions such that the newly-defined integral operator is starlike, convex and close-to-convex, respectively. The example given at the end of the paper proves the applicability of the obtained results.

Suggested Citation

  • Georgia Irina Oros, 2021. "Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2539-:d:652847
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    References listed on IDEAS

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    1. Lupaş, Alina Alb & Oros, Gheorghe, 2015. "On special fuzzy differential subordinations using Sălăgean and Ruscheweyh operators," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 119-127.
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    Cited by:

    1. Ekram Elsayed Ali & Miguel Vivas-Cortez & Shujaat Ali Shah & Abeer M. Albalahi, 2023. "Certain Results on Fuzzy p -Valent Functions Involving the Linear Operator," Mathematics, MDPI, vol. 11(18), pages 1-10, September.
    2. Sorin Nădăban, 2022. "Fuzzy Logic and Soft Computing—Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921–2017)," Mathematics, MDPI, vol. 10(17), pages 1-3, September.

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    1. Alina Alb Lupaş & Georgia Irina Oros, 2021. "New Applications of Sălăgean and Ruscheweyh Operators for Obtaining Fuzzy Differential Subordinations," Mathematics, MDPI, vol. 9(16), pages 1-12, August.
    2. Daniel Breaz & Shahid Khan & Ferdous M. O. Tawfiq & Fairouz Tchier, 2023. "Applications of Fuzzy Differential Subordination to the Subclass of Analytic Functions Involving Riemann–Liouville Fractional Integral Operator," Mathematics, MDPI, vol. 11(24), pages 1-22, December.
    3. Georgia Irina Oros & Simona Dzitac, 2022. "Applications of Subordination Chains and Fractional Integral in Fuzzy Differential Subordinations," Mathematics, MDPI, vol. 10(10), pages 1-18, May.

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