We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

Notions of quasi-classical Lie-super algebra as well as Lie-super triple systems have been given and studied with some examples. Its application to Yang-Baxter equation has also been given. 1991 Mathematics Subject Classification Primary 17A40, 17B60

In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W -mappings of a countable family of ...

in this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex banach space. we establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.

In this paper, we first show that the iteration {xn} defined by xn+1 = P ((1−αn)xn +αnTP [βnTxn + (1− βn)xn]) converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with err...

Inclusion relations for k−uniformly starlike functions under the Dziok-Srivastava operator are established. These results are also extended to k−uniformly convex functions, close-to-convex, and quasi-convex functions.

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.