and Applied Analysis 3 4 strictly η-monotone if 〈 u − v, ηx, y > 0, ∀x, y ∈ H, x / y, u ∈ M x , v ∈ M ( y ) ; 2.5 5 strongly monotone if there exists a constant r > 0 satisfying 〈 u − v, x − y ≥ r∥x − y∥2, ∀x, y ∈ H, u ∈ M x , v ∈ My; 2.6 6 strongly η-monotone if there exists a constant r > 0 satisfying 〈 u − v, ηx, y ≥ r∥x − y∥2, ∀x, y ∈ H, u ∈ M x , v ∈ My; 2.7 7 maximal monotone resp., maxim...

We introduce a flexible lifetime distribution called Burr III-Inverse Weibull (BIII-IW). The new proposed distribution has well-known sub-models. The BIII-IW density function includes exponential, left-skewed, right-skewed and symmetrical shapes. The BIII-IW model’s failure rate can be monotone and non-monotone depending on the parameter values. To show the importance of the BIII-IW distributio...

Monotone and multiply monotone densities have well-known mixture representations. The underlying mixture representations give rise to a wide variety of fascinating inverse problems. We review the forward problems (estimation of the mixed density) and the inverse problems (estimation of the mixing distribution in two different guises), including Hampel’s bird resting time problem and generalizat...

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and Applied Analysis 3 where A n = α n I + A for all n ≥ 0. In particular, if V ≡ 0, then (11) reduces to the following iterative scheme: x 0 = x ∈ C chosen arbitrarily, y n = P C (x n − ] n A n x n ) , z n = β n x n + γ n P C (x n − ] n A n y n ) + σ n TP C (x n − ] n A n y n ) , x n+1 = P C [λ n (1 − δ n ) γSx n + (I − λ n μF) z n ] , ∀n ≥ 0. (12) Further, if S = V, then (11) reduces to the f...

An explicit hierarchical fixed point algorithm is introduced to solve the monotone variational inequality over the fixed point set of a nonexpansive mapping. This paper discusses a monotone variational inequality with variational constraint and convex optimization problems over the fixed point set of a nonexpansive mapping. The strong convergence for the proposed algorithm to the solution is gu...

In this paper, we consider a proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in real Hilbert spaces. Also, we give a necessary and sufficient condition for the common zero set of finite operators to be nonempty, and by showing that in this case, this iterative sequence converges strongly to the metric projection of some point onto the set of c...

Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this note we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient algorithms. F...

where F is a monotone operator. Recently, Lu et al. [] were concerned with a special class of variational inequalities in which the mapping F is the complement of a nonexpansive mapping and the constraint set is the set of fixed points of another nonexpansive mapping. Namely, they considered the following type of monotone variational inequality (VI) problem: Find x∗ ∈ Fix(T), such that 〈(I –V ...