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Some inequalities involving multivalent functions

Shigeyoshi Owa, Mamoru Nunokawa, Hitoshi Saitoh (1994)

Annales Polonici Mathematici

The object of the present paper is to derive some inequalities involving multivalent functions in the unit disk. One of our results is an improvement and a generalization of a result due to R. M. Robinson [4].

Some lower bounds for the quotients of normalized error function and their partial sums

Basem Aref Frasin (2025)

Archivum Mathematicum

The purpose of the present paper is to determine lower bounds for k f ( z ) ( k f ) m ( z ) , ( k f ) m ( z ) k f ( z ) , k ' f ( z ) ( k f ) m ' ( z ) and ( k f ) m ' ( z ) k ' f ( z ) , where k f is the generalized normalized error function of the form k f z = z + n = 2 - 1 n - 1 ( n - 1 k + 1 ) n - 1 ! z n and ( k f ) m its partial sum. Furthermore, we give lower bounds for 𝕀 k f ( z ) ( 𝕀 k f ) m ( z ) and ( 𝕀 k f ) m ( z ) 𝕀 k f ( z ) , where 𝕀 k f is the Alexander transform of k f . Several examples of the main results are also considered.

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