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Journal of Interdisciplinary Mathematics cover

Journal of Interdisciplinary Mathematics

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502
CiteScore 2025: 1.9 (Q2)

CiteScore 2025: 1.9 (Q2)

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Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Journal of Interdisciplinary Mathematics
Open Access Research Article

New class of normalized multivalent harmonic functions

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pp. 859–864Vol. 28Issue 3-AApril 2025DOI: 10.47974/JIM-2014XML
Received:
09 Oct 2024
Published Online:
08 May 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2014
Pages:
859–864

Abstract

Let H(m) be the class of functions of the form f(z) = h(z) + g(z),  where f is a harmonic function in a open unit disk U’ = {z ∈ ₵ :|z|<1}. Here, g is the co-analytic part and h is the analytic part of f. The function f is locally univalent in U’ if |g’(z)|<|h’(z)| for all z ∈ U’, which is the necessary and sufficient condition. A function f belongs to SH(m) if it is an m-valently harmonic function, where SH(m) is a subclass of functions f ∈ H(m). Additionally, if  Jf =|h`|2 –|g`|2 > 0 in U’, then the functions in SH(m) are harmonic and sense-preserving in U’. This paper introduces new classes for normalized multivalent harmonic function within an open unit disk U’ = {z ∈ ₵ :|z|<1}, providing a detailed analysis of these functions. The authors investigate properties such as coefficient bounds, which are critical in understanding the behavior of these functions. By normalizing these multivalent harmonic functions, they simplify their form, making it easier to derive and analyze this property. The paper also establishes bounds on the coefficients of the series expansions of these functions, offering significant insights into their structure and limitations. Relevant connections of the results presented here with various known results are briefly indicated.

Keywords

Harmonic functionsAnalytic functionsMultivalent functionsCoefficient estimates

Subject Classifications

32A50

References

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