Lemniscate Convexity and Other Properties of Generalized Bessel\n Functions

2019/02/12 by Vibha Madaan, Ajay Kumar, Madaan, Vibha +3 · 1 citation
Mathematics · #30C10 #30C45 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.1902.04277

openalex publication_date 2019/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Sufficient conditions on associated parameters p,b and c are obtained so\nthat the generalized and textquotedblleftnormalized textquotedblright\nBessel function u_p(z)=u_p,b,c(z) satisfies\n|(1+(zu''_p(z)/u'_p(z)))²-1|<1 or |((zu_p(z))'/u_p(z))²-1|<1. We also\ndetermine the condition on these parameters so that\n-(4(p+(b+1)/2)/c)u'_p(z) prec\√(1+z). Relations between the parameters\n\μ and p are obtained such that the normalized Lommel function of first\nkind h_\μ,p(z) satisfies the subordination\n1+(zh''_\μ,p(z)/h'_\μ,p(z)) prec\√(1+z). Moreover, the properties of\nAlexander transform of the function h_\μ,p(z) are discussed.\n

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