[Show abstract][Hide abstract] ABSTRACT: This paper deals with the existence of solutions for a class of nonlinear implicit variational inclusion problems in semi-inner product spaces. We construct an iterative algorithm for approximating the solution for the class of implicit variational inclusions problems involving A-monotone and H-monotone operators by using the generalized resolvent operator technique.
Applied Mathematics and Computation 06/2014; 236:109–117. · 1.35 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this paper, the numerical range for two operators (both linear and nonlinear) have
been studied in semi-inner product spaces. The inclusion relations between numerical
range, approximate point spectrum, compression spectrum, eigenspectrum, and spectrum
have been established for two linear operators. We also show the inclusion relation between
approximate point spectrum and closure of the numerical range for two nonlinear
operators. An approximation method for solving the operator equation involving two
nonlinear operators is also established.
Abstract and Applied Analysis 01/2012; 2012. · 1.10 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this paper, multi-objective programming (MOP) approaches are proposed to deal with the feasible vertical block linear complementarity problems (VLCP) and to look into the solvability and unsolvability of the VLCP. The characterization of an unsolvable VLCP is obtained via the existence of nonzero efficient point of the MOP problem. Also a perturbed problem is proposed if the VLCP is unsolvable for small disturbances in data. This perturbed problem is useful to construct the solvable VLCP corresponding to the original unsolvable VLCP. Examples are given to demonstrate the effectiveness of the results.
Journal of Information & Optimization Sciences. 03/2010; 31(2).
[Show abstract][Hide abstract] ABSTRACT: We study some extensions of Hardy-Hilbert’s inequality with an improved weight coefficient. We also establish reverse inequalities of Hardy-Hilbert-type inequalities.
Communications in Applied Analysis 01/2010; 14(4).
[Show abstract][Hide abstract] ABSTRACT: The purpose of this paper is to discuss and obtain some basic theoretical results for the variational inequality problems in the most general setting for topological vector spaces. Some relationship between variational inequality and complementarity problems have been established. Several results known in the literature are obtained as special cases of our results.
International Journal of Optimization: Theory, Methods and Applications. 01/2010; 2(2).
[Show abstract][Hide abstract] ABSTRACT: In this paper we have studied somenew inequalities similar to Hardy-Hilbert's inequal- ity. As applications, we have considered the associated integral inequalities.
Mathematical Inequalities and Applications 01/2010; · 0.59 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper presents Opial inequalities for fractional derivatives of integrable functions. The inequalities are proved for integrable functions using the index law for fractional derivatives
International Journal of Modern Mathematics. 01/2009; 4(3).
[Show abstract][Hide abstract] ABSTRACT: This paper develops a solution method for chance constrained programming problem, where the random variable in the right hand side of the chance constraints follows different fuzzy distributions. The methodology is verified through numerical examples.
International Journal of Optimization: Theory, Methods and Applications. 01/2009; 1(1).
[Show abstract][Hide abstract] ABSTRACT: In this paper, we establish sufficiency criteria under generalized ρ−(η,θ)ρ−(η,θ)-invexity conditions for general continuous-time programming problems with nonlinear equality/inequality constraints. Using this we establish some existence criteria for solutions of a class of variational-type inequalities.
Mathematical and Computer Modelling 06/2008; 47:1332-1338. · 1.42 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper deals with a chance constrained programming model, where both fuzziness and randomness are present in the objective
function and constraints. The concept of fuzzy random variable, mean and variance of fuzzy random variable, minimum of fuzzy
numbers are used in the model. The methodology is verified through a numerical example.
Fuzzy Optimization and Decision Making 01/2008; 7:59-74. · 1.49 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: By the Hilbert inequality the authors mean the inequality stating that the integral operator with the kernel 1 x+y on (0,∞) is bounded in L p . What is called the Hilbert-Pachpatte inequality is a similar inequality which envolves derivatives and the kernel is 1 x 2n-2k+1 +y 2n-2k+1 and p=2. The authors prove some generalizations of the latter inequality for fractional derivatives, technically too complicated to be reproduced here. The main feature of these generalizations is the admission of variable exponents. Reviewer’s remark: The “Hölder type” inequality for variable exponents stated in Lemma 1.4, and used in the proofs, is more rough than the actually known Hölder inequality for variable exponents, which for the one-dimensional case was proved in 1979 in [I. I. Sharapudinov, Math. Notes 26, 796–806 (1980); translation from Mat. Zametki 26, 613–632 (1979; Zbl 0437.46024), see also O. Kovacik and J. Rakosnik, Czech. Math. J. 41(116), No. 4, 592–618 (1991; Zbl 0784.46029)]. Lebesgue spaces with variable exponents were an object of study in many papers during the last two decades, where various deep results on inequalities with such exponents were obtained, of which the authors seem to be unaware. We refer for instance to the reviewer’s surveying paper [Integr. Transf. Spec. Funct. 16, No. 5–6, 461–482 (2005; Zbl 1069.47056)].
International Journal of Modern Mathematics. 01/2008; 3(1).
[Show abstract][Hide abstract] ABSTRACT: In this paper several kinds of (ρ,θ)-η-invariant-monotone functions and generalized (ρ,θ)-η-invariant-monotone functions are considered. For a given Frechet differentiable function f,∇f (gradient of f), (ρ,θ)-η-invariant-monotonicity of ∇f is related to (ρ,θ)-η-invexity of f. It is also shown that (ρ,θ)-η-invariant-monotonicity and generalized (ρ,θ)-η-invariant-monotonicity are proper generalizations of invariant-monotonicity and generalized invariant-monotonicity.
[Show abstract][Hide abstract] ABSTRACT: In this paper, solutions of horizontal linear complementarity problems (HLCP) are studied using multi-objective programming and the fuzzy approach. The multiobjective programming based approach either solves the HLCP or under certain condition shows that the HLCP is unsolvable. The approximate solution of the infeasible HLCP can then be obtained to some degree of satisfaction when a minimum relaxation is allowed in the inequality and equality relations of the given problem. Also some examples are provided and discussed.
[Show abstract][Hide abstract] ABSTRACT: This paper deals with a methodology for solving a chance constrained fuzzy linear programming problem. The methodology is applied to the chance constrained model where the constraints have two different types of fuzzy inequalities and the method is justified through numerical examples.
[Show abstract][Hide abstract] ABSTRACT: In this paper we study some relations between (ρ,θ)-η-B-vexity and (ρ,θ)-η-B- vex sets in a real Banach space X. In particular we also establish some of the relations between (ρ,θ)-η-B-invexity and (ρ,θ)-η -preinvexity in a real Banach space X.
Mathematical Inequalities and Applications 01/2007; 10(2). · 0.59 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The parametric vertical block linear complementarity problem is introduced where the associated vertical block matrix and the column vector are parametric. Assuming the matrix to be a vertical block P-matrix, an algorithm is developed for solving vertical block linear complementarity problems. A necessary and sufficient condition is also derived to ensure the same solution basis for any parametric input of the vertical block P-matrix. Based on these, an algorithm is proposed and the solution of the parametric vertical block linear complementarity problem is obtained. A numerical example is presented to illustrate the use of the method.