Ruscheweyh Derivative and a New Generalized
Operator Involving Convolution

Ezekiel Abiodun Oyekan; S.R. Swamy; Timothy Oloyede Opoola

doi:https://doi.org/10.14445/22315373/IJMTT-V67I1P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 1 | Year 2021 | Article Id. IJMTT-V67I1P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I1P513

Ruscheweyh Derivative and a New Generalized Operator Involving Convolution

Ezekiel Abiodun Oyekan, S.R. Swamy, Timothy Oloyede Opoola

Citation :

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 (IJMTT), vol. 67, no. 1, pp. 88-100, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I1P513

Abstract

In this present investigation, we introduce a generalized differential operator 𝛦𝛼,𝛽 𝑚 (𝜇,𝜑,𝑡)via convolution approach. Using this operator, we further introduced a new generalized differential operator 𝑅𝛦𝛼,𝛽,𝛿 𝑚 (𝜎,𝜑,𝑡)𝑓(𝑧) obtained as a linear combination of Ruscheweyh derivative and the operator 𝛦𝛼,𝛽 𝑚 (𝜇, 𝜑,𝑡). With the aid of the new generalized differential operator, a new subclass ℳ𝛼,𝛽,𝛿 𝑚,𝜆,𝜇,𝜎,𝜑,𝑡 (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.

Keywords

analytic function, differential operator, distortion theorem, multiplier transformation

References

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