Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
A new general integral operator defined by Al-Oboudi differential operator - MaRDI portal

A new general integral operator defined by Al-Oboudi differential operator (Q1008477)

From MaRDI portal





scientific article; zbMATH DE number 5534609
Language Label Description Also known as
English
A new general integral operator defined by Al-Oboudi differential operator
scientific article; zbMATH DE number 5534609

    Statements

    A new general integral operator defined by Al-Oboudi differential operator (English)
    0 references
    0 references
    30 March 2009
    0 references
    The author defines a new integral operator as follows: Let \(k\in \mathbb{N}_0\), \(l=(l_{1},\dots ,l_{n})\in \mathbb{N}_{0}^{n}\), and \(\mu_{i}>0\, ,\, 1\leq i\leq n\, .\) One defines an integral operator \(I_{k,n,l,\mu}: A^{n}\rightarrow A\) by \[ I_{k,n,l,\mu}(f_{1},\dots ,f_{n})=F, \] \[ \displaystyle{D^{k}F(z)= \int_{0}^{z} \left (\frac{D^{l_{1}}f_{1}(t)}{t}\right )^{\mu_{1}} \dots \left ( \frac{D^{l_{n}}f_{n}(t)}{t}\right )^{\mu_{n}} dt}\, , \] where \(f_{1}\, ,\, \dots\, ,\, f_{n}\in A\) and \(D\) is the Al-Oboudi differential operator. Also he introduces new subclasses of analytic functions and gives some results concerning the integral operator \(I_{k,n,l,\mu}\) on the above mentioned subclasses. The results presented on this paper generalize some results of M. Acu, D. Breaz, H.O. Guney and Gr. Salagean.
    0 references
    0 references
    Integral operator
    0 references
    Al-Oboudi differential operator
    0 references

    Identifiers