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Bianchi-Type VI0 Bulk Viscous Fluid Models with Variable Gravitational and Cosmological Constants  [PDF]
Manoj K. Verma, Shri Ram
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.23041
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.
Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis
Ram U. Verma
International Journal of Mathematics and Mathematical Sciences , 2009, DOI: 10.1155/2009/691952
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.
G-H-KKM selections with applications to minimax theorems
Ram U. Verma
International Journal of Stochastic Analysis , 2000, DOI: 10.1155/s1048953300000265
Abstract: Based on the G-H-KKM selections, some nonempty intersection theorems and their applications to minimax inequalities are presented.
Sensitivity analysis for relaxed cocoercive nonlinear quasivariational inclusions
Ram U. Verma
International Journal of Stochastic Analysis , 2006, DOI: 10.1155/jamsa/2006/52041
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.
-monotonicity and applications to nonlinear variational inclusion problems
Ram U. Verma
International Journal of Stochastic Analysis , 2004, DOI: 10.1155/s1048953304403013
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.
Partially relaxed cocoercive variational inequalities and auxiliary problem principle
Ram U. Verma
International Journal of Stochastic Analysis , 2004, DOI: 10.1155/s1048953304305010
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*〉
Convergence estimates and approximation solvability of nonlinear implicit variational inequalities
Ram U. Verma
International Journal of Stochastic Analysis , 2002, DOI: 10.1155/s1048953302000047
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.
A class of nonlinear variational inequalities involving pseudomonotone operators
Ram U. Verma
International Journal of Stochastic Analysis , 2000, DOI: 10.1155/s1048953300000071
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.
Linear Convergence Analysis for General Proximal Point Algorithms Involving (H,η)- Mo notonicity Frameworks
Verma,Ram U;
Cubo (Temuco) , 2011, DOI: 10.4067/S0719-06462011000300010
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.
The e -Optimality Conditions for Multiple Objective Fractional Programming Problems for Generalized Descripción: http:/fbpe/img/cubo/v14n2/art01-01.jpg- Invexity of Higher Order
Verma,Ram U;
Cubo (Temuco) , 2012, DOI: 10.4067/S0719-06462012000200001
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.
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