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    STUDIA MATHEMATICA - Issue no. 3 / 2023  
         
  Article:   NEW SUBCLASSES OF BI-UNIVALENT FUNCTIONS CONNECTED WITH A Q-ANALOGUE OF CONVOLUTION BASED UPON THE LEGENDRE POLYNOMIALS.

Authors:  SHEZA M. EL-DEEB, BASSANT M. EL-MATARY.
 
       
         
  Abstract:  DOI: 10.24193/subbmath.2023.3.06

Received 13July 2020; Accepted 30 October 2020. Published Online: 2023-09-30
Published Print: 2023-09-30
pp. 527-542

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In this paper, we introduce new subclasses of analytic and bi-univalent functions connected with a q-analogue of convolution by using the Legendre polynomials. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients /a2/ and /a3/ for functions in these subclasses and obtain Fekete-Szegő problem for these subclasses.

Mathematics Subject Classification (2010): 30C50, 30C45, 11B65, 47B38.
Keywords: Legendre polynomials, convolution, q-analogue of Pascal distribution, q-analogue of poission operator, bi-univalent, coefficients bounds.
 
         
     
         
         
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