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April 18, 2026Journal of Mathematics0 citationsOpen Access

Initial Coefficient Bounds of Convex Functions Related to Pascal Snail Function

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AFArooj FatimaURUmar RazaASAfis Saliu

Key Points

  • To establish initial coefficient bounds for a specific class of convex functions related to the Pascal snail function.
  • Defined a subclass of convex functions using subordination relations.
  • Analyzed coefficient bounds for functions in the identified class.
  • Determined bounds on Hankel determinants | H 2,1 ( f )| and | H 2,2 ( f )|.
  • Initial coefficient bounds for the convex functions were presented.
  • Sharp bounds on Hankel determinants were established.

Abstract

For −1 ≤ λ ≤ 1, let be a subclass of convex functions associated with the Pascal snail function, analytically defined by the subordination relation, (1 + τ f ″ ( τ )/ f ′ ( τ ))≺1/(1 − λ τ ). In this article, we have presented the initial coefficient bounds for the functions f in the class . We have also established the bounds on the Hankel determinants | H 2,1 ( f )| and | H 2,2 ( f )| for this class. Most of the bounds presented are sharp.

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Cite This Study

Fatima et al. (2026) studied this question.

synapsesocial.com/papers/69e3209340886becb653fa25https://doi.org/10.1155/jom/3671812
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