Third order differential subordination and superordination results for analytic functions involving the Hohlov operator

Mishra, Akshaya; Prajapati, A.; Gochhayat, P.

doi:10.32513/tbilisi/1601344901

Cited by 5 publications

(3 citation statements)

References 28 publications

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“…Recently, by making use of Hohlov operator Gochhayat et al (cf. [29]) have derived various third order differential subordination and superordination related results. In this investigation, by considering suitable classes of admissible functions, we obtained some interesting inclusion results on third order differential subordination and superordination involving S a,c .…”

Section: Definition 3 [[5]mentioning

confidence: 99%

Applications of third order differential subordination and superordination involving generalized struve function

Gochhayat

Prajapati

2019

Filomat

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Section: Definition 3 [[5]mentioning

confidence: 99%

Applications of third order differential subordination and superordination involving generalized struve function

Gochhayat

Prajapati

2019

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“…The generalized Bessel functions [33,35], generalized Mittag-Leffler functions [29], Liu-Srivastava operator [34], a fractional operator [15], and Srivastava-Attiya operator [32] are all connected to third-order differential subordination in fascinating new ways. Third-order differential subordination research is still active, with recent publications using the Hohlov operator [18], Generalized Hurwitz-Lerch Zeta Functions [6], and many additional operators [8,9,12]. Third-order differential subordination research is continuing to add to the knowledge regarding second-order differential subordination [28].…”

Section: Introductionmentioning

confidence: 99%

Introduction in third-order fuzzy differential subordination

OROS,

GÜNEY

2024

Hacettepe Journal of Mathematics and Statistics

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In light of the well-established and widely-used theory of differential subordination, recent works incorporating fuzzy elements into Geometric Function Theory have given rise to the concept of fuzzy differential subordination. Second-order fuzzy differential subordinations were taken into consideration for studies up until this point. The research described in this paper aims to expand the concept of fuzzy differential subordination to third-order fuzzy differential subordination, building on an idea first put forth in 2011 by José A. Antonino and Sanford S. Miller and still being investigated by scholars today. The key concepts and preliminary findings required for the development of this branch of fuzzy differential subordination are introduced. The class of admissible functions is specified, the fundamental theorems are established and the fundamental concepts of the third-order fuzzy subordination approach are presented. The example given demonstrates the applicability of the new findings.

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“…The two dual theories of third-order differential subordination and superordination continue to develop nicely. Very recent results obtained using this approach can be found in papers like [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

New Developments on the Theory of Third-Order Differential Superordination Involving Gaussian Hypergeometric Function

Oros,

Preluca

2023

Mathematics

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The present research aims to present new results regarding the fundamental problem of providing sufficient conditions for finding the best subordinant of a third-order differential superordination. A theorem revealing such conditions is first proved in a general context. As another aspect of novelty, the best subordinant is determined using the results of the first theorem for a third-order differential superordination involving the Gaussian hypergeometric function. Next, by applying the results obtained in the first proved theorem, the focus is shifted to proving the conditions for knowing the best subordinant of a particular third-order differential superordination. Such conditions are determined involving the properties of the subordination chains. This study is completed by providing means for determining the best subordinant for a particular third-order differential superordination involving convex functions. In a corollary, the conditions obtained are adapted to the special case when the convex functions involved have a more simple form.

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Third order differential subordination and superordination results for analytic functions involving the Hohlov operator

Cited by 5 publications

References 28 publications

Applications of third order differential subordination and superordination involving generalized struve function

Applications of third order differential subordination and superordination involving generalized struve function

Introduction in third-order fuzzy differential subordination

New Developments on the Theory of Third-Order Differential Superordination Involving Gaussian Hypergeometric Function

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