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...

In this paper, we define and study convergence of an Ishikawa type iteration scheme with a new and weaker control condition for two nonself asymptotically quasi-nonexpansive mappings on a uniformly convex Banach space.

We show constructively that every quasi-convex uniformly continuous function f : C → R+ has positive infimum, where C is a convex compact subset of Rn. This implies a constructive separation theorem for convex sets.

Themain purpose of this paper is to introduce a new hybrid iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, set of common fixed points of a family of quasi-φ-asymptotically nonexpansivemappings, and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach...

In this paper, we introduce a new iterative procedure which is constructed by the modified block hybrid projection method for solving a common solution of fixed point problems for two countable families of uniformly total quasi-φ-asymptotically nonexpansive and uniformly Lipschitz continuous mappings. Under suitable conditions, some strong convergence theorems are established in a uniformly smo...

In this paper we propose two strongly convergent parallel hybrid iterative methods for finding a common element of the set of fixed points of a family of asymptotically quasi φ-nonexpansive mappings, the set of solutions of variational inequalities and the set of solutions of equilibrium problems in uniformly smooth and 2-uniformly convex Banach spaces. A numerical experiment is given to verify...

In this paper, a new iterative scheme by hybrid method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of an infinite family of relatively quasi-nonexpansive mappings and set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. Our results extend important recent ...

In this paper, we introduce a new modified block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-j-asymptotically nonexpansive mappings, the set of the variational inequality for an a-inverse-strongly monotone operator, and the set of solutions of a system of generalized mixed equilibrium problems. We obtain ...

and Applied Analysis 3 In this paper, we generalize and modify the iteration of Abbas et al. 7 from two mapping to the infinite family mappings {Ti : i ∈ N} of multivalued quasi-nonexpansive mapping in a uniformly convex Banach space. Let {Ti} be a countable family of multivalued quasi-nonexpansive mapping from a bounded and closed convex subset K of a Banach space into P K with F : ⋂∞ i 1 F Ti...

We estimate the decay of correlations for some Markov maps on a countable states space. A necessary and suucient condition is given for the transfer operator to be quasi-compact on the space of locally Lipschitz functions. In the non quasi-compact case, the decay of correlations depends on the contribution to the transfer operator of the complementary of nitely many cylinders. Estimates are giv...