Rassias. Th.M., Noor, M.A. and Noor, K.I. (2018) Auxiliary Principle Technique for the General Lax-Milgram Lemma. Journal of Nonlinear Functional Analysis, 2018, Article No. 34.
https://doi.org/10.23952/jnfa.2018.34

has been cited by the following article:

• TITLE: Some New Systems of Exponentially General Equations

  AUTHORS: Muhammad Aslam Noor, Khalida Inayat Noor

  KEYWORDS: General Equations, Lax-Milgram Lemma, Auxiliary Principle, Iterative Method, Convergence

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.12 No.3, September 30, 2022

  ABSTRACT: Some new systems of exponentially general equations are introduced and investigated, which can be used to study the odd-order, non-positive and nonsymmetric exponentially boundary value problems. Some important and interesting results such as Riesz-Frechet representation theorem, Lax-Milgram lemma and system of absolute values equations can be obtained as special cases. It is shown that the system of exponentially general equations is equivalent to nonlinear optimization problem. The auxiliary principle technique is used to prove the existence of a solution to the system of exponentially general equations. This technique is also used to suggest some new iterative methods for solving the system of the exponentially general equations. The convergence analysis of the proposed methods is analyzed. Ideas and techniques of this paper may stimulate further research.