We investigate the problem of pointwise convergence of the family of non-linear integral operators: \begin{equation} L_\lambda(f,x) = \int_a^b \sum_{m=1}^N f^m(t) K_{\lambda ,m}(x,t) dt, \end{equation} where $\lambda $ is a real parameters, $K_{\lambda ,m}(x,t)$ is non-negative kernel and $f$ is the function in $L_{1}(a,b)$. We consider two cases where $% (a,b)$ is a finite interval and when is the whole real axis.

In this paper, an Inventory model with unit production cost, time depended holding cost, with-out shortages is formulated and solved. We have considered a single objective structural optimization model. In most real world situation, the objective and constraint function of the decision makers are\nimprecise in nature. Hence the coefficients, indices, the objective function and\nconstraint goals are imposed here in fuzzy environment. Geometric programming\nprovides a powerful tool for solving a variety of imprecise optimization problems. Here we use nearest interval approximation method to convert a triangular fuzzy number to an interval\nnumber. In this paper, we transform this interval number to a parametric\ninterval-valued functional form and then solve the parametric problem by\ngeometric programming technique. Numerical example is given to illustrate the\nmodel through this Parametric Geometric-Programming method.

In this paper, we develop some modifications of the multiplicative Newton method which are third-order convergence. We use the multiplicative Newton Theorem and Newton Cotes quadrature formulas to present these new modifications of the multiplicative Newton method. Using the multiplicative Taylor expansion, we give also the convergence analysis of these new methods. Furthermore, we compare the multiplicative Newton methods with the classical Newton methods in details.

We investigate a predator-prey model for egg-eating predators in which the prey population is assumed to have an age structure. By the method of characteristics, this model reduces to a system of integral equations. Then a generalization of the Banach fixed-point theorem is used to show, under relatively mild conditions, the existence of a unique, global, weak solution to the population problem. Furthermore, this methodology allows us to generate a sequence of iterates, called the Picard iterates, that converges to the solution. Also, we strengthen the assumptions of the existence-uniqueness theorem to establish the validity of the corresponding conservation law in integral form. Thus we prove a result which shows the coexistence of both predator and prey species over a long time.

In this paper, the Laplace transform of the distribution of the duration of a particular semi-Markovian random walk period is obtained in the form of the difference equation.

In this study, complex differential equations are solved using laplace transform. Firstly we seperate real and imaginer parts of equation. Thus from one unknown equation is obtained two unknown equation system. Later we obtain laplace transforms of real and imaginer parts of solutions using laplace transform. In the latest we obtain real and imaginer parts of solution using inverse laplace transform.

In this paper, we obtain some results on the dimension of the isometry group of a Riemannian manifold. In specific dimensions, we give a range which the dimension of an isometry group can not be in. We also give necessary conditions for a manifold to have a free canonical action on some specific manifolds. We give a boundary of the dimension of the full isometry group if the dimension of a manifold is greater or equal to 4.

The purpose of this article is to introduce the notion of (C 1 ,C 2 )-Hlder Krull valuation on right ring of fractions ( with respect to right denominator set S in a ring R). It is proved that if R is a ring satisfying in Hlder rigidity condition, and S a right permutable set of regular elements in R, then the right ring of fractions R = Q r (R) with respect to S satisfies in Hlder rigidity condition. This results provide an extension of the Garsia theorem (see

Some basic properties in connection to generalized relative order and generalized relative lower order of entire functions have been discussed in this paper.

In this study, complex differential equations are solved using laplace transform. Firstly we seperate real and imaginer parts of equation. Thus from one unknown equation is obtained two unknown equation system. Later we obtain laplace transforms of real and imaginer parts of solutions using laplace transform. In the latest we obtain real and imaginer parts of solution using inverse laplace transform.