Semigroup Research Papers - Academia.edu (original) (raw)

An integral representation of the operator semigroup that corresponds to the most general nonbreaking Feller process on a line that is pasted from two diffusion processes is constructed, by using analytical methods.

We show that generalizations of some (classical) results on the Hyers-Ulam stabil- ity of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable.

We define an equivalence relation on a topological space which is acted by topological monoidSas a transformation semigroup. Then, we give some results about theS-invariant classes for this relation. We also provide a condition for the... more

We define an equivalence relation on a topological space which is acted by topological monoidSas a transformation semigroup. Then, we give some results about theS-invariant classes for this relation. We also provide a condition for the existence of relativeS-invariant classes.

Distribution semigroup in the sense of Wang and Kunstmana and the properties of infinitesimal generator are considered with in exponentially bounded distributions. Results are applied on a class of equations of the form (?/?t)4-An = ?, ?... more

Distribution semigroup in the sense of Wang and Kunstmana and the properties of infinitesimal generator are considered with in exponentially bounded distributions. Results are applied on a class of equations of the form (?/?t)4-An = ?, ? ? ?+1 (L(e)), where D(A) c L?(R) or D(A) c E = Cb(R).

A semigroup S is said to be monotone if its binary operation is a monotone function from S × S into S. This paper utilizes some of the known algebraic structure of Clifford semigroups, semigroups which are unions of groups, to study... more

A semigroup S is said to be monotone if its binary operation is a monotone function from S × S into S. This paper utilizes some of the known algebraic structure of Clifford semigroups, semigroups which are unions of groups, to study topological Clifford semigroups which are monotone. It is shown that such semigroups are preserved under products, homomorphisms, and, under certain conditions, closures. Necessary and sufficient conditions for monotonicity of groups, paragroups, bands, compact orthodox Clifford semigroups, and compact bands of groups are developed.

Recently, Olaleru and Okeke [19] introduced the class of asymptotically demicon- tractive mappings in the intermediate sense as a generalization of the class of asymptotically demicontractive mappings. The authors proved some convergence... more

Recently, Olaleru and Okeke [19] introduced the class of asymptotically demicon- tractive mappings in the intermediate sense as a generalization of the class of asymptotically demicontractive mappings. The authors proved some convergence theorems for this class of nonlinear mappings in Hilbert spaces (see, [19]). The purpose of this paper is to continue the study of this class of nonlinear mappings. We prove some fixed point theorems for the class of asymptotically demicontractive mappings in the intermediate sense. We also prove some mean convergence theorems for this class of mappings in Hilbert spaces.

We study existence of a unique mild solution of evolution quantum stochastic differential equations with nonlocal conditions under the strong topology. Using the method of successive approximations, we do not need to transform the... more

We study existence of a unique mild solution of evolution quantum stochastic differential equations with nonlocal conditions under the strong topology. Using the method of successive approximations, we do not need to transform the nonlocal problem to a fixed point form. The evolution operator A generates a family of semigroup that are continuous. Nonlocal conditions allow additional measurements of certain phenomena that cannot be captured by the traditional initial conditions. We show that under some given conditions, the mild solution is unique and also stable. The method applied here is much easier when compared with previous methods used in literature.

In this paper, we present the concepts of the upper and lower approximations of Anti-rough subgroups, Anti-rough subsemigroups, and homeomorphisms of Anti-Rough anti-semigroups in approximation spaces. Specify the concepts of rough in... more

In this paper, we present the concepts of the upper and lower approximations of Anti-rough subgroups, Anti-rough subsemigroups, and homeomorphisms of Anti-Rough anti-semigroups in approximation spaces. Specify the concepts of rough in Finite anti-groups of types (4) are studies. Moreover, some properties of approximations and these algebraic structures are introduced. In addition, we give the definition of homomorphism anti-group.

In this paper, we continue our previous research studies of exponential ultradistribution semigroups in Banach spaces. The existence and uniqueness of analytical solutions of abstract fractional relaxation equations associated with the... more

In this paper, we continue our previous research studies of exponential ultradistribution semigroups in Banach spaces. The existence and uniqueness of analytical solutions of abstract fractional relaxation equations associated with the generators of exponential ultradistribution semigroups have been considered. Some other results are also proved.

In this paper we prove the existence and uniqueness for the solution to a stochastic reaction–diffusion equation, defined on a network, and subjected to nonlocal dynamic stochastic boundary conditions. The result is obtained by deriving a... more

In this paper we prove the existence and uniqueness for the solution to a stochastic reaction–diffusion equation, defined on a network, and subjected to nonlocal dynamic stochastic boundary conditions. The result is obtained by deriving a Gaussian-type estimate for the related leading semigroup, under rather mild regularity assumptions on the coefficients. An application of the latter to a stochastic optimal control problem on graphs, is also provided.