Certain subclasses of multivalent functions defined by new multiplier transformations

zbMATH Open1289.30101arXiv1008.4702MaRDI QIDQ5326629

Erhan Deniz, Halit Orhan

Publication date: 6 August 2013

Abstract: In the present paper the new multiplier transformations $mathrm{mathcalJ\mathrm{\%}}_p^{delta}(lambda,mu,l)$ $$ of multivalent functions is defined. Making use of the operator $mathrm{\mathrm{\%}mathcalJ}_p^{delta}(lambda,mu,l),$ two new subclasses $mathcal{\mathrm{\%}P}_{lambda,mu,l}^{delta}(A,B;sigma,p)$ and $widetildemathcalP{\mathrm{\%}}_{lambda,mu,l}^{delta}(A,B;sigma,p)$ extbf{ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses $mathcal{P}_{lambda,mu,l}^{delta}(A,B;sigma,p)$ and $widetilde{mathcalP}_{lambda,mu,l}^{delta}(A,B;sigma,p)$ are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.

Full work available at URL: https://arxiv.org/abs/1008.4702

zbMATH Keywords

analytic functionKoebe domainconic domainlinear multiplier fractional differential operatordistortion and rotation theorems

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Coefficient problems for univalent and multivalent functions of one complex variable (30C50)

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