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On special fuzzy differential subordinations using Sălăgean and Ruscheweyh operators

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  • Lupaş, Alina Alb
  • Oros, Gheorghe

Abstract

In the present paper we establish several fuzzy differential subordinations regarding the operator Lαm, given by Lαm:A→A,Lαmf(z)=(1−α)Rmf(z)+αSmf(z), where Rmf(z) denote the Ruscheweyh derivative, Smf(z) is the Sălăgean operator and An={f∈H(U),f(z)=z+an+1zn+1+⋯,z∈U} is the class of normalized analytic functions with A1=A. A certain fuzzy class, denoted by SLFm(δ,α), of analytic functions in the open unit disk is introduced by means of this operator. By making use of the concept of fuzzy differential subordination we will derive various properties and characteristics of the class SLFm(δ,α). Also, several fuzzy differential subordinations are established regarding the operator Lαm.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:261:y:2015:i:c:p:119-127
    DOI: 10.1016/j.amc.2015.03.087
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    Cited by:

    1. 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.
    2. Georgia Irina Oros, 2021. "Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    3. 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.
    4. 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.

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