An operator associated with the Wright function is introduced in the open unit disk. Differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. In particular, some inequalities for modified Bessel functions are also obtained.

In this paper, we propose a genetic algorithm, called GenSPN, for finding highly probable differential characteristics of substitution permutation networks (SPNs). A special fitness function and a heuristic mutation operator have been used to improve the overall performance of the algorithm. We report our results of applying GenSPN for finding highly probable differential characteristics of Ser...

in present paper acertain convolution operator of analytic functions is defined.moreover, subordination- and superordination- preserving propertiesfor a class of analytic operators defined on the space of normalizedanalytic functions in the open unit disk is obtained. we also applythis to obtain sandwich results and generalizations of some knownresults.

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

in this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in f(t,x(t))dt +g(t,x(t))dw_t$ in which the multifunction $f$ is semimonotone and hemicontinuous and the operator-valued multifunction $g$ satisfies a lipschitz condition. we define the it^{o} stochastic integral of operator set-valued stochastic pr...

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...

‎in the present paper‎, ‎by making use of the differential subordination and‎ ‎superordination results of miller and mocanu‎, ‎  ‎certain classes of admissible functions ‎are determined so that subordination as well as superordination implications‎ ‎of functions associated with an integral operator hold‎. ‎additionally‎, ‎differential sandwich-type result is obtained‎.

‎In the present paper‎, ‎by making use of the differential subordination and‎ ‎superordination results of Miller and Mocanu‎, ‎  ‎certain classes of admissible functions ‎are determined so that subordination as well as superordination implications‎ ‎of functions associated with an integral operator hold‎. ‎Additionally‎, ‎differential sandwich-type result is obtained‎.

In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.