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.

In recent years increasing interests and considerable researches have been given to the fractional differential equations both in time and space variables. These are due to the applications of the fractional differential operators to problems in a wide areas of physics and engineering science and a rapid development of the corresponding theory. Motivating examples include the so-called continuo...

We apply the method of operator splitting on the generalized Korteweg{de Vries (KdV) equation ut +f(u)x+"uxxx = 0, by solving the nonlinear conservation law ut +f(u)x = 0 and the linear dispersive equation ut + "uxxx = 0 sequentially. We prove that if the approximation obtained by operator splitting converges, then the limit function is a weak solution of the generalized KdV equation. Convergen...

The equation Lu f , where L A B, with A being a K-positive definite operator and B being a linear operator, is solved in a Banach space. Our scheme provides a generalization to the so-called method of moments studied in a Hilbert space by Petryshyn 1962 , as well as Lax and Milgram 1954 . Furthermore, an application of the inverse function theorem provides simultaneously a general solution to t...

By definition, the coefficient sequence c = (cn) of a d’Alembertian series — Taylor’s or Laurent’s — satisfies a linear recurrence equation with coefficients in C(n) and the corresponding recurrence operator can be factored into first order factors over C(n) (if this operator is of order 1, then the series is hypergeometric). Let L be a linear differential operator with polynomial coefficients....

We consider solutions of the non-linear von Neumann equation involving Jacobi’s elliptic functions sn, cn, and dn, and 3 linearly independent operators. In two cases one can construct a state-dependent Hamiltonian which is such that the corresponding non-linear von Neumann equation is solved by the given density operator. We prove that in a certain context these two cases are the only possibili...

Decoding a fractal compressed image can be seen as solving an aane two-scale functional equation. If the aane term is zero, the dilation equation becomes linear and the solution is similar to the scaling functions from wavelet theory. In both cases a linear operator, parameter-ized with a few variables determines a complicate looking function. We present two classes of algorithms for gray image...

Decoding a fractal compressed image can be seen as solving an a ne two-scale functional equation. If the a ne term is zero, the dilation equation becomes linear and the solution is similar to the scaling functions from wavelet theory. In both cases a linear operator, parameterized with a few variables determines a complicate looking function. We present two classes of algorithms for gray image ...