Abstract:
This paper deals with Bianchi type VI0 anisotropic cosmological models filled with a bulk viscous cosmic fluid in the presence of time-varying gravitational and cosmological constant. Physically realistic solutions of Einstein's field equations are obtained by assuming the conditions 1) the expansion scalar is proportional to shear scalar 2) the coefficient of the bulk viscosity is a power function of the energy density and 3) the cosmic fluid obeys the barotropic equation of state. We observe that the corresponding models retain the well established features of the standard cosmology and in addition, are in accordance with recent type Ia supernovae observations. Physical behaviours of the cosmological models are also discussed.

Abstract:
Based on a notion of relatively maximal (m)-relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing Rockafellar's theorem (1976) on linear convergence using the proximal point algorithm in a real Hilbert space setting. Convergence analysis, based on this new model, is simpler and compact than that of the celebrated technique of Rockafellar in which the Lipschitz continuity at 0 of the inverse of the set-valued mapping is applied. Furthermore, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution equations as well as evolution inclusions.

Abstract:
Some results on the sensitivity analysis for relaxed cocoercive quasivariational inclusions are obtained, which generalize similar sensitivity analysis results on strongly monotone quasivariational inclusions. Furthermore, some suitable examples of relaxed cocoercive mappings are illustrated.

Abstract:
A new notion of the A-monotonicity is introduced, which generalizes the H-monotonicity. Since the A-monotonicity originates from hemivariational inequalities, and hemivariational inequalities are connected with nonconvex energy functions, it turns out to be a useful tool proving the existence of solutions of nonconvex constrained problems as well.

Abstract:
Let T:K→H be a mapping from a nonempty closed convex subset K of a finite-dimensional Hilbert space H into H. Let f:K→ℝ be proper, convex, and lower semicontinuous on K and let h:K→ℝ be continuously Frećhet-differentiable on K with h′ (gradient of h), α-strongly monotone, and β-Lipschitz continuous on K. Then the sequence {xk} generated by the general auxiliary problem principle converges to a solution x* of the variational inequality problem (VIP) described as follows: find an element x*∈K such that 〈T(x*),x−x*〉

Abstract:
Approximation-solvability of a class of nonlinear implicit variational inequalities involving a class of partially relaxed monotone mappings - a computation-oriented class in a Hilbert space setting- is presented with some applications.

Abstract:
We present the solvability of a class of nonlinear variational inequalities involving pseudomonotone operators in a locally convex Hausdorff topological vector spaces setting. The obtained result generalizes similar variational inequality problems on monotone operators.

Abstract:
general framework for the generalized proximal point algorithm, based on the notion of (h,r)- monotonicity, is developed. the linear convergence analysis for the generalized proximal point algorithm to the context of solving a class of nonlinear variational inclusions is examined, the obtained results generalize and unify a wide range of problems to the context of achieving the linear convergence for proximal point algorithms.

Abstract:
motivated by the recent investigations in literature, a general framework for a class of -invex n-set functions of higher order is introduced, and then some results on the e-optimality conditions for multiple objective fractional subset programming are explored. the obtained results are general in nature, while generalize and unify results on generalized invexity as well as on generalized invexity of higher order to the context of multiple fractional programming.