In this paper, we propose an explicit viscosity approximation method for finding a common element of the set of fixed points of strict pseudo-contractions and of the set of solutions of variational inequalities with inverse-strongly monotone mappings. Strong convergence theorems are established in the framework of Hilbert spaces. 2000 Mathematics Subject Classification: 47H05, 47H09, 47J25

We show that strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are so that all solutions converge to a unique equilibrium. The result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. An application to a reaction of interest in biochemistry is provided as an illustration.

In this paper, we introduce a general viscosity-type extragradient method for solving the fixed point problem of an asymptotically nonexpansive mapping and variational inclusion with two accretive operators. We obtain strong convergence theorem in setting Banach spaces. terms theorem, establish result (FPP) inequality (VIP) inverse-strongly monotone framework Hilbert Finally, is applied to deal...

In real Hilbert spaceH , from an arbitrary initial point x0 ∈H , an explicit iteration scheme is defined as follows: xn+1 = αnxn + (1 − αn)Tn+1xn,n ≥ 0, where Tn+1xn = Txn − λn+1μF(Txn), T :H →H is a nonexpansive mapping such that F(T) = {x ∈ K : Tx = x} is nonempty, F :H →H is a η-strongly monotone and k-Lipschitzian mapping, {αn} ⊂ (0,1), and {λn} ⊂ [0,1). Under some suitable conditions, the ...

In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.Then, we give two new iterative methods  by combining the resolvent method with Halpern's iterative method and viscosity approximation method for  finding a fixed point of monotone mappings and a solution of variational inequalities. We prove convergence theorems of the proposed iterations  in ...

In this paper a new class of mappings, known as locally λ-strongly φ-accretive mappings, where λ and φ have special meanings, is introduced. This class of mappings constitutes a generalization of the well-known monotone mappings, accretive mappings and strongly φ-accretive mappings. Subsequently, the above notion is used to extend the results of Park and Park, Browder and Ray to locally λ-stron...