bounded functionsWe show that the class MATH ${\\\mathfrak{E}_0}$ of analytic functions in a plane region MATH $\\\Omega otin {O_{AB}}$ vanishing at MATH ${z_0} \\\in \\\Omega$ and such that omits a set of values of area is not compact. Here denotes the class of Riemann...
doi:10.1155/2013/923167We define a new subclassby using an integral operator . We find a coefficient inequality and using that we derive many sharp results. These results generalize many results which are existing in the literature.JOURNAL OF MECHANICSPravati SahooSaumya Singh...
Mathematics(GeneralWe define a new subclass M ( ?? , ?? , ?? , ?? ) by using an integral operator Q ?? ?? f ( z ) . We find a coefficient inequality and using that we derive many sharp results. These results generalize many results which are existing in the literature....
Suppose that is an analytic function in a domain, , of finite connectivity. We give a criterion for a decomposition of , as a polynomial of another function, that is restricted to a continuum in , to extend to the rest of . We show by examples that this criterion cannot be improved. ...
Let A denote the class of functions of the form f(z)=z+∑ n=2 ∞ a n z n that are regular in U={z:|z|<1}. For 0≤α<1, let S α (z)=z/(1-z) 2-2α . The authors introduce the class R λ,αδ (A,B) of functions f in A that satisfy |e iδ (f*S α (...
a n ( z ??? w ) n which are univalent in the unit disc U = { z ??? ??? : | z | < 1 } . In this paper, we obtain coefficient inequalities, distortion theorem, closure theorems, and class preserving integral operators of functions belonging to the class S m , w * ( ??
For 0<\lambda \le 1, let {\mathcal {U}}( \lambda ) be the class of analytic functions in the unit disk \mathbb {D} with f(0)=f'(0)-1=0 satisfying | f'(z) (z/f(z))^2 -1 | < \lambda in \mathbb {D}. Then, it is known that every f \in {\mathcal {U}}( \...
For an expanding real matrix M=[ρ−1C0ρ−1]∈M2(R) and a digit set D={(0,0)t,(1,0)t,(0,1)t}, let μM,D be the self-affine measure generated by M and D. In this paper, we show that L2(μM,D) admits an infinite orthogonal set of exponential functions if and onl...
An It^o calculus for a class of limit processes arising from random walks on the complex plane An It^o calculus for a class of limit processes arising from random walks on the complex planeMathematics - ProbabilityWithin the framework of the ... S Bonaccorsi,C Calcaterra,S Mazzucchi 被引...
Let A be the class of normalized analytic functions in the unit disk Δ, F ( a , b ; c ; z ) and Φ ( a ; c ; z ) denote respectively, the Gaussian and con... S Ponnusamy - 《Journal of Computational & Applied Mathematics》 ...