Ruscheweyh Derivative and a New Generalized Operator Involving Convolution

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-1
Year of Publication : 2021
Authors : Ezekiel Abiodun Oyekan, S.R. Swamy, Timothy Oloyede Opoola
  10.14445/22315373/IJMTT-V67I1P513

MLA

MLA Style: Ezekiel Abiodun Oyekan, S.R. Swamy, Timothy Oloyede Opoola  "Ruscheweyh Derivative and a New Generalized Operator Involving Convolution" International Journal of Mathematics Trends and Technology 67.1 (2021):88-100. 

APA Style: Ezekiel Abiodun Oyekan, S.R. Swamy, Timothy Oloyede Opoola(2021). Ruscheweyh Derivative and a New Generalized Operator Involving Convolution  International Journal of Mathematics Trends and Technology, 88-100.

Abstract
In this present investigation, we introduce a generlized differential operator Emα,β(μ,Φ,t) via convolution approach. Using this operator, we further introduced a new generalized differential operator REmα,β,δ(σ,φ,t)f(Z) obtained as a linear combination of Ruscheweyh derivative and the operator Emα,β(μ,Φ,t). With the aid of the new generalized differential operator, a new subclass Mm,λ,μ,σ,φ,tα,β,δ (ρ) of analytic functions in the open unit disk is introduced and investigated. Characterization and other properties of this class are studied. In particular, Coefficient estimates, distortion theorems of functions with negative coefficients belonging to this class are also determined. Some relevant remarks and useful connections of the main results are also pointed out.     

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Keywords : analytic function, differential operator, distortion theorem, multiplier transformation.