In this article, we consider an analytic $ p $-valent function $ f_{p}(\zeta) $ blended with a power series which has the probabilities of the Pascal distribution as its coefficients. Using the subordination principle, the subclasses $ S^{*}_{s}(p, \alpha, \delta; I, J) $ and $ S^{*}_{sc}(p, \alpha, \delta; I, J) $ are defined with respect to other points, and some properties (such as coefficient estimates, growth and distortion properties, radii of starlikeness, convexity, extreme points) of the function belonging to the aforementioned subclasses are investigated. Additionally, some consequences of the results obtained are discussed as corollaries.
Citation: Hamzat Jamiu Olusegun, Abbas Kareem Wanas, Daniel Breaz. Some results on new subclasses of regular $ p $-valent functions blended with Pascal distribution series defined with respect to other points[J]. AIMS Mathematics, 2026, 11(9): 29312-29326. doi: 10.3934/math.20261165
In this article, we consider an analytic $ p $-valent function $ f_{p}(\zeta) $ blended with a power series which has the probabilities of the Pascal distribution as its coefficients. Using the subordination principle, the subclasses $ S^{*}_{s}(p, \alpha, \delta; I, J) $ and $ S^{*}_{sc}(p, \alpha, \delta; I, J) $ are defined with respect to other points, and some properties (such as coefficient estimates, growth and distortion properties, radii of starlikeness, convexity, extreme points) of the function belonging to the aforementioned subclasses are investigated. Additionally, some consequences of the results obtained are discussed as corollaries.
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Hamzat Jamiu Olusegun, Abbas Kareem Wanas, Daniel Breaz. Some results on new subclasses of regular $ p $-valent functions blended with Pascal distribution series defined with respect to other points[J]. AIMS Mathematics, 2026, 11(9): 29312-29326. doi: 10.3934/math.20261165
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