Strong Subordination for P-Valent Functions Involving A Linear Operator

Hadi, Enaam; Atshan, Waggas Galib

doi:10.1088/1742-6596/1818/1/012113

Cited by 8 publications

(5 citation statements)

References 2 publications

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“…There have been many interesting and fruitful usages of a wide variety of first-order and second-order strong differential subordinations for analytic functions. Recently, many researchers have worked in this direction and proved several significant results that can be seen in [6][7][8]. Various strong differential subordinations were established by linking different types of operators to the study.…”

Section: Introduction and Definitionsmentioning

confidence: 95%

Results of Third-Order Strong Differential Subordinations

Soren,

Wanas,

Cotîrlǎ

2024

Axioms

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In this paper, we present and investigate the notion of third-order strong differential subordinations, unveiling several intriguing properties within the context of specific classes of admissible functions. Furthermore, we extend certain definitions, presenting novel and fascinating results. We also derive several interesting properties of the results of third-order strong differential subordinations for analytic functions associated with the Srivastava–Attiya operator.

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Section: Introduction and Definitionsmentioning

confidence: 95%

Results of Third-Order Strong Differential Subordinations

Soren,

Wanas,

Cotîrlǎ

2024

Axioms

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“…). We denote by Q * the set of functions that are analytic and injective on U × Results involving strong differential superordination investigated with operators began to be published shortly after the concept was introduced [9], continued to demonstrate the topic's interest in the following years ( [10,11]) and are still in development, as evidenced by the numerous papers published in recent years ( [12][13][14][15][16][17]). The differential operator studied in [18] was extended in the paper published in 2012 [19] to the new class of analytic functions A * nζ using the definitions given below.…”

Section: Definition 3 ([7]mentioning

confidence: 99%

Strong Differential Superordination Results Involving Extended Sălăgean and Ruscheweyh Operators

Lupaş

Oros

2021

Mathematics

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The notion of strong differential subordination was introduced in 1994 and the theory related to it was developed in 2009. The dual notion of strong differential superordination was also introduced in 2009. In a paper published in 2012, the notion of strong differential subordination was given a new approach by defining new classes of analytic functions on U×U¯ having as coefficients holomorphic functions in U¯. Using those new classes, extended Sălăgean and Ruscheweyh operators were introduced and a new extended operator was defined as Lαm:Anζ*→Anζ*,Lαmf(z,ζ)=(1−α)Rmf(z,ζ)+αSmf(z,ζ),z∈U,ζ∈U¯, where Rmf(z,ζ) is the extended Ruscheweyh derivative, Smf(z,ζ) is the extended Sălăgean operator and Anζ*={f∈H(U×U¯), f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}. This operator was previously studied using the new approach on strong differential subordinations. In the present paper, the operator is studied by applying means of strong differential superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential superordinations concerning the operator Lαm are established and the best subordinant is given for each strong differential superordination.

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“…The best dominant for a strong differential subordination, and the dual notion, the best subordinant of a strong differential superordination, were established in [8], and first examples of strong differential subordinations and superordinations of analytic functions were given in [9]. Since then, there have been results regarding strong differential subordination and superordination with well-known operators: Liu-Srivastava operator [10], Sȃlȃgean differential operator [11], Ruscheweyh derivative [12] and combinations between Sȃlȃgean and Ruscheweyh operators [13], Komatu integral operator [14,15], multiplier transformation [16,17], general differential operators [18,19], and many others well-known operators [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

Lupaş

2023

Symmetry

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In 2012, new classes of analytic functions on U×U¯ with coefficient holomorphic functions in U¯ were defined to give a new approach to the concepts of strong differential subordination and strong differential superordination. Using those new classes, the extended Dziok–Srivastava operator is introduced in this paper and, applying fractional integral to the extended Dziok–Srivastava operator, we obtain a new operator Dz−γHmlα1,β1 that was not previously studied using the new approach on strong differential subordinations and superordinations. In the present article, the fractional integral applied to the extended Dziok–Srivastava operator is investigated by applying means of strong differential subordination and superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential subordinations and superordinations concerning the operator Dz−γHmlα1,β1 are established, and the best dominant and best subordinant are given for each strong differential subordination and strong differential superordination, respectively. This operator may have symmetric or asymmetric properties.

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Strong Subordination for P-Valent Functions Involving A Linear Operator

Cited by 8 publications

References 2 publications

Results of Third-Order Strong Differential Subordinations

Results of Third-Order Strong Differential Subordinations

Strong Differential Superordination Results Involving Extended Sălăgean and Ruscheweyh Operators

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

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