Subordination and superordination results associated with the generalized hypergeometric function

Magesh, Nanjundan; Jothibasu, Jagadeesan; Murthy, Sami

doi:10.2478/s12175-014-0269-8

Cited by 4 publications

(4 citation statements)

References 25 publications

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“…Motivated by the numerous allowances of the fractional derivative operators which have newly been reflected by many authors, here, we purposed two operators involving the generalized hypergeometric-type function and the generalized Beta function. Various studies can be found in [12,13,14].…”

Section: Resultsmentioning

confidence: 99%

Studies on Fractional Differential Operators of Two Parameters in a Complex Domain

Ibrahim¹,

Jalab²

2016

TJANT

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This study deals with a generalization for fractional differential operators in a complex domain based on the extended Beta function. Stipulations are imposed for these generalized operators such as the upper bounds. Other possessions for the above operator are also prepared. In addition, implementations of these operators are introduced and suggested in the geometric function theory (GFT). Sufficient conditions are imposed for functions to be univalent.

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Section: Resultsmentioning

confidence: 99%

Studies on Fractional Differential Operators of Two Parameters in a Complex Domain

Ibrahim¹,

Jalab²

2016

TJANT

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“….. Not much study was done using differential superordination theory on confluent hypergeometric function. Some superordination results were obtained for the generalized hypergeometric function as it can be seen in papers [9][10][11] some superordination results were stated in the form of sandwich-type theorems.…”

Section: Definition 3 ([3])mentioning

confidence: 99%

Applications of Inequalities in the Complex Plane Associated with Confluent Hypergeometric Function

Oros

2021

Symmetry

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The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called the theory of differential subordination or admissible functions theory. Later, in 2003, a particular form of inequality in the complex plane was also defined by them as dual notion for subordination, the notion of differential superordination and with it, the theory of differential superordination appeared. In this paper, the theory of differential superordination is applied to confluent hypergeometric function. Hypergeometric functions are intensely studied nowadays, the interest on the applications of those functions in complex analysis being renewed by their use in the proof of Bieberbach’s conjecture given by de Branges in 1985. Using the theory of differential superodination, best subordinants of certain differential superordinations involving confluent (Kummer) hypergeometric function are stated in the theorems and relation with previously obtained results are highlighted in corollaries using particular functions and in a sandwich-type theorem. An example is also enclosed in order to show how the theoretical findings can be applied.

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“…Magesh et al. ( 2014 ) studied the subordination and superordination results of the linear operator denoted by . Also, they discussed the sufficient condition to satisfy for some convex functions and with and and are analytic functions in with …”

Section: Introductionmentioning

confidence: 99%

Differential inequalities imposed by the extended hypergeometric function

2016

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Recently, the generalized hypergeometric function is extended by utilizing the Beta function. Based on this type of function, we introduce a new operator in the open unit disk. The present article investigates some subordination and superordination results for certain normalized analytic functions in the open unit disk, which are acted upon by the generalized Noor integral operator. Some of outcomes improve and generalize previously known outcomes.

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Subordination and superordination results associated with the generalized hypergeometric function

Cited by 4 publications

References 25 publications

Studies on Fractional Differential Operators of Two Parameters in a Complex Domain

Studies on Fractional Differential Operators of Two Parameters in a Complex Domain

Applications of Inequalities in the Complex Plane Associated with Confluent Hypergeometric Function

Differential inequalities imposed by the extended hypergeometric function

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