Harmonic mappings related to the bounded boundary rotation

Kahramaner, Yasemin; Polatoğlu, Yaşar

doi:10.12988/ijma.2014.410306

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2018

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“…For various related classes, we refer [1,2,3,8,9,12,13,14,15,24]. For f ∈ A , we consider the following one parameter families of integral operators…”

Section: Introductionmentioning

confidence: 99%

Some applications of certain integral operators involving functions

Noor¹,

Malik²,

Bukhari³

2018

Tamkang J. Math.

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Abstract.Integral transforms map equations from their original domains into others where manipulations and solutions may be much easier than in original domains. To get back in the original environment, we use the idea of inverse of the integral transform. A function analytic and locally univalent in a given simply connected domain is said to be of bounded boundary rotation if its range has bounded boundary rotation which is defined as the total variation of the direction angle of the tangent to the boundary curve under a complete circuit.The main objective of the present article is to study some applications of certain integral operators to functions of bounded radius rotation involving Janowski functions. We discuss some inclusion results under certain assumption on parameters involve in operators as well as in related subclasses of analytic functions. Most of these results are best possible. We also relate our findings with the existing literature of the subjects.

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“…For various related classes, we refer [1,2,3,8,9,12,13,14,15,24]. For f ∈ A , we consider the following one parameter families of integral operators…”

Section: Introductionmentioning

confidence: 99%