Muhammad Noor

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Muhammad Aslam

Rabia Kamal

IOBM

Salahuddin Salahuddin

muhammad noor

HUZOOR KHAN

Aligarh Muslim University

Muhammad S

Hassan Riahi

Université Cadi Ayyad

muhammad noor

Gheorghe Morosanu

Central European University

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Papers by Muhammad Noor

Sensitivity Analysis for Quasi-Variational Inclusions

Journal of Mathematical Analysis and Applications, 1999

In this paper, we develop the sensitivity analysis for quasi variational inclusions by using the ... more

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Numerical solutions of a system of fourth order boundary value problems

International Journal of Computer Mathematics, 1998

It is known that contact, obstacle and unilateral problems arising in different branches of pure ... more It is known that contact, obstacle and unilateral problems arising in different branches of pure and applied sciences can be studied in the framework of variational inequalities. In this paper, we show that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational equations, which are solved using finite difference method derived by Pade' approximant.

Variational iteration technique for solving higher order boundary value problems

Applied Mathematics and Computation, 2007

In this paper, we have shown that higher order boundary value problems can be written as a system... more In this paper, we have shown that higher order boundary value problems can be written as a system of integral equations, which can be solved by using the variational iteration technique. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the method. Comparisons are made to confirm the reliability of the technique. Variational iteration technique may be considered as alternative and efficient for finding the approximate solutions of the boundary values problems.

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Homotopy perturbation method for solving sixth-order boundary value problems

Computers & Mathematics With Applications, 2008

We apply the homotopy perturbation method for solving the fourth-order boundary value problems. T... more We apply the homotopy perturbation method for solving the fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of the method. Homotopy method can be considered an alternative method to Adomian decomposition method and its variant forms.

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An efficient method for fourth-order boundary value problems

Computers & Mathematics With Applications, 2007

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Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems

Mathematical Problems in Engineering, 2007

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An efficient algorithm for solving fifth-order boundary value problems

Mathematical and Computer Modelling, 2007

In this paper, we apply the homotopy perturbation method for solving the fifth-order boundary val... more In this paper, we apply the homotopy perturbation method for solving the fifth-order boundary value problems. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of the method.

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Quartic spline method for solving fourth order obstacle boundary value problems

Journal of Computational and Applied Mathematics, 2002

In this paper, we use uniform quartic polynomial splines to develop a new method, which is used f... more In this paper, we use uniform quartic polynomial splines to develop a new method, which is used for computing approximations to the solution and its ÿrst, second as well as third derivatives for a system of fourth order boundary value problems associated with obstacle, unilateral and contact problems. It is shown that the present method is of order two and gives approximations which are better than those produced by other collocation and ÿnite di erence methods. Numerical examples are presented to illustrate the applicability of the new method. (E.A. Al-Said), [email protected] (M.A. Noor).

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Some developments in general variational inequalities

Applied Mathematics and Computation, 2004

General variational inequalities provide us with a unified, natural, novel and simple framework t... more General variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of equilibrium problems arising in pure and applied sciences. In this paper, we present a number of new and known numerical techniques for solving general variational inequalities using various techniques including projection, Wiener-Hopf equations, updating the solution, auxiliary principle, inertial proximal, penalty function, dynamical system and well-posedness. We also consider the local and global uniqueness of the solution and sensitivity analysis of the general variational inequalities as well as the finite convergence of the projection-type algorithms. Our proofs of convergence are very simple as compared with other methods. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems. Since the general variational inequalities include (quasi) variational inequalities and (quasi) implicit complementarity problems as special cases, results presented here continue to hold for these problems. Several open problems have been suggested for further research in these areas.

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Three-Step Iterative Algorithms for Multivalued Quasi Variational Inclusions

Journal of Mathematical Analysis and Applications, 2001

In this paper, we suggest and analyze some new classes of three-step iterative algorithms for sol... more In this paper, we suggest and analyze some new classes of three-step iterative algorithms for solving multivalued quasi variational inclusions by using the resolvent equations technique. New iterative algorithms include the Ishikawa, Mann, and Noor iterations for solving variational inclusions (inequalities) and optimization problems as special cases. The results obtained in this paper represent an improvement and a significant refinement of previously known results.

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General algorithm and sensitivity analysis for variational inequalities

Journal of Applied Mathematics and Stochastic Analysis, 1992

The fixed point technique is used to prove the existence of a solution for a class of variational... more The fixed point technique is used to prove the existence of a solution for a class of variational inequalities related to odd order boundary value problems, and to suggest a general algorithm. We also study the sensitivity analysis for these variational inequalities and complementarity problems using the projection technique. Several special cases are discussed, which can be obtained from our results.

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Generalized Set-Valued Variational Inclusions and Resolvent Equations

Journal of Mathematical Analysis and Applications, 1998

In this paper, we establish the equivalence between the generalized set-valued variational inclus... more In this paper, we establish the equivalence between the generalized set-valued variational inclusions, the resolvent equations, and the fixed-point problem, using the resolvent operator technique. This equivalence is used to suggest and analyze some iterative algorithms for solving the generalized set-valued variational inclusions and related optimization problems. ᮊ 1998 Academic Press

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New Approximation Schemes for General Variational Inequalities

Journal of Mathematical Analysis and Applications, 2000

In this paper, we suggest and consider a class of new three-step approximation schemes for genera... more

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Set-Valued Resolvent Equations and Mixed Variational Inequalities

Journal of Mathematical Analysis and Applications, 1998

In this paper, we introduce and study a new class of variational inequalities, which is called th... more In this paper, we introduce and study a new class of variational inequalities, which is called the generalized set-valued mixed variational inequality. The resolvent operator technique is used to establish the equivalence among generalized set-valued variational inequalities, fixed point problems, and the generalized setvalued resolvent equations. This equivalence is used to study the existence of a solution of set-valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems. The results proved in this paper represent a significant refinement and improvement of the previously known results in this area.

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Some aspects of variational inequalities

In this paper we provide an account of some of the fundamental aspects of variational inequalitie... more

On Integral Operators

Journal of Mathematical Analysis and Applications, 1999

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Self-adaptive projection algorithms for general variational inequalities

Applied Mathematics and Computation, 2004

In this paper, we consider and analyze a new class of self-adaptive projection algorithms for sol... more

Merit functions for general variational inequalities

Journal of Mathematical Analysis and Applications, 2006

In this paper, we consider some classes of merit functions for general variational inequalities. ... more In this paper, we consider some classes of merit functions for general variational inequalities. Using these functions, we obtain error bounds for the solution of general variational inequalities under some mild conditions. Since the general variational inequalities include variational inequalities, quasivariational inequalities and complementarity problems as special cases, results proved in this paper hold for these problems. In this respect, results obtained in this paper represent a refinement of previously known results for classical variational inequalities.  2005 Elsevier Inc. All rights reserved.

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General variational inequalities and nonexpansive mappings

Journal of Mathematical Analysis and Applications, 2007

In this paper, we suggest and analyze some three-step iterative schemes for finding the common el... more In this paper, we suggest and analyze some three-step iterative schemes for finding the common elements of the set of the solutions of the Noor variational inequalities involving two nonlinear operators and the set of the fixed points of nonexpansive mappings. We also consider the convergence analysis of the suggested iterative schemes under some mild conditions. Since the Noor variational inequalities include variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as an refinement and improvement of the previously known results.

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New extragradient-type methods for general variational inequalities

Journal of Mathematical Analysis and Applications, 2003

In this paper, we consider and analyze a new class of extragradient-type methods for solving gene... more In this paper, we consider and analyze a new class of extragradient-type methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is weaker condition than monotonicity. Our proof of convergence is very simple as compared with other methods. The proposed methods include several new and known methods as special cases. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems.  2002 Elsevier Science (USA). All rights reserved.

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Sensitivity Analysis for Quasi-Variational Inclusions

Journal of Mathematical Analysis and Applications, 1999

In this paper, we develop the sensitivity analysis for quasi variational inclusions by using the ... more

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Numerical solutions of a system of fourth order boundary value problems

International Journal of Computer Mathematics, 1998