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Mathematics
Article . 2020 . Peer-reviewed
License: CC BY
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Mathematics
Article
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Mathematics
Article . 2020
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Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points

Authors: Muhammad Arif; Omar Barkub; Hari Srivastava; Saleem Abdullah; Sher Khan;

Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points

Abstract

The motive behind this article is to apply the notions of q-derivative by introducing some new families of harmonic functions associated with the symmetric circular region. We develop a new criterion for sense preserving and hence the univalency in terms of q-differential operator. The necessary and sufficient conditions are established for univalency for this newly defined class. We also discuss some other interesting properties such as distortion limits, convolution preserving, and convexity conditions. Further, by using sufficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic functions to its sequences of partial sums. Some known consequences of the main results are also obtained by varying the parameters.

Keywords

harmonic function, QA1-939, Janowski starlike functions, q-derivative operator, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
37
Top 10%
Top 10%
Top 10%
gold