and Applied Analysis 3 nonexpansive mapping such that F S ∩ A−10/ ∅. Let {xn} be a sequence generated by x0 x ∈ C and un J−1 ( βnJxn ( 1 − βn ) JSJrnxn ) , Cn { z ∈ C : φ z, un ≤ φ z, xn } , Qn {z ∈ C : 〈xn − z, Jx0 − Jxn〉 ≥ 0}, xn 1 ΠCn∩Qnx0 1.6 for all n ∈ N ∪ {0}, where J is the duality mapping on E, {βn} ⊂ 0, 1 , and {rn} ⊂ a,∞ for some a > 0. If lim infn→∞ 1 − βn > 0, then {xn} converges s...

We develop a new class of schemes for the numerical solution of first-order steady conservation laws. The schemes are of the residual distribution, or fluctuation-splitting type. These schemes have mostly been developed in the context of triangular or tetrahedral elements whose degrees of freedom are their nodal values. We work here with more general elements that allow high-order accuracy. We ...

Extending the characterization of the directional derivatives of a strongly regular solution to a variational inequality under parameter perturbations, this paper derives a first-order sensitivity result for a monotone-plus affine variational inequality (AVI) having non-isolated solutions. The result employs a “directional AVI” whose solutions provide the directional derivatives, if they exist,...

In this paper, we introduce a new iterative sequence which is constructed by using the hybrid projection method for solving the common solution for a system of generalized equilibrium problems of inverse strongly monotone mappings and a system of bifunctions satisfying certain the conditions, the common solution for the families of quasi -φasymptotically nonexpansive and uniformly Lipschitz con...

A new monotonicity, M-monotonicity, is introduced, and the resolvant operator of an M-monotone operator is proved to be single-valued and Lipschitz continuous. With the help of the resolvant operator, the positively semidefinite general variational inequality (VI) problem VI (S+,F +G) is transformed into a fixed point problem of a nonexpansive mapping. And a proximal point algorithm is construc...

The employment of proper codings, such as the base-2 coding, has allowed to establish the universal approximation property of Boolean functions: if a sufficient number b of inputs (bits) is taken, they are able to approximate arbitrarily well any real Borel measurable mapping. However, if the reduced set of monotone Boolean functions, whose expression involves only and and or operators, is cons...

Following the work of Shida, Shindoh, and Kojima and of Monteiro and Zanjacomo, we study the issue of existence and uniqueness of search directions in interior-point methods for the monotone LCP over the space of n n symmetric block-diagonal matrices, with particular focus on the direction of Alizadeh, Haeberly, and Overton (AHO). We give an ana-log of a result of Shida et al., characterizing e...

Manuscript received January 01, 2014; revised March 28, 2014. This work was supported in part by King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. Cyril Dennis Enyi is with King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. (corresponding author: +966550782390; e-mail: cenyi@ kfupm.edu.sa). Mukiawa Edwin Soh is with King Fahd University of Petroleum and ...

We consider energy-conserving semi-discretizations of linear wave equations on nonuniform grids. Specifically we study explicit and implicit skew-adjoint finite difference methods, based on the assumption of an underlying smooth mapping from a uniform grid, applied to the first and second order wave equations. Our interest is in internal reflection of energy at abrupt variations in grid spacing...

We present the strong convergence theorem for the iterative scheme for finding a common element of the fixed-point set of a quasi-nonexpansive mapping and the zero set of the sums of maximal monotone operators in Hilbert spaces. Our results extend and improve the recent results of Takahashi et al. (J. Optim. Theory Appl. 147:27-41, 2010) and Takahashi and Takahashi (Nonlinear Anal. 69:1025-1033...