In this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{T}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. We use a strong convolution technique and derive inclusion results. A radius problem and some other interesting properties of these classes are discussed.

In this paper, we defined two classes $S_{p}^{ast }(n,lambda ,A,B)$ and\ $ K_{p}(n,lambda ,A,B)$ of meromorphic $p-$valent functions associated with a new linear operator. We obtained convolution properties for functions in these classes.

Let ∑ p be the class of functions f(z) which are analytic in the punctured disk E∗ = {z ∈ C : 0 < |z| < 1}. Applying the linear operator Dn+p defined by using the convolutions, the subclass n+p(α) of ∑ p is considered. The object of the present paper is to prove that n+p(α) ⊂ n+p−1(α). Since 0(α) is the class of meromorphic p-valent starlike functions of order α, all functions in n+p−1(α) are m...

Nevanlinna theory [Ne] was created to give a quantitative measure of the value distribution for meromorphic functions, for instance to measure the extent to which they approximate a finite number of points. We view a meromorphic function as a holomorphic map ƒ : C —• P into the projective line. The theory has various higher dimensional analogues, of which we shall later consider maps ƒ : C —• X...

We study (i) asymptotic behaviour of wild harmonic bundles, (ii) the relation between semisimple meromorphic flat connections and wild harmonic bundles, (iii) the relation between wild harmonic bundles and polarized wild pure twistor D-modules. As an application, we show the hard Lefschetz theorem for algebraic semisimple holonomic D-modules, conjectured by M. Kashiwara. We also study resolutio...

In this paper, we obtain a normal criterion of meromorphic functions concerning shared values. Let D be a domain in C and F be a family of meromorphic functions in D. Let k, n,m ∈ N, n ≥ mk+m+1, and a, b two finite complex numbers with a 6= 0. Suppose that every f ∈ F has all its zeros of multiplicity at least k+ 1 . If f + a(f ) and g + a(g)share the value b IM for every pair of functions (f, ...