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Computation of solution of integral equations via fixed point results

Alqudah Manar A., Garodia Chanchal, Uddin Izhar, Nieto Juan J.

Demonstratio Mathematica

2022

Vol. 55, nr 1

772--785

The motive of this article is to study a modified iteration scheme for monotone nonexpansive mappings in the class of uniformly convex Banach space and establish some convergence results. We obtain weak and strong convergence results. In addition, we present a nontrivial numerical example to show the convergence of our iteration scheme. To demonstrate the utility of our scheme, we discuss the solution of nonlinear integral equations as an application, which is again supported by a nontrivial example.

Generalized vector quasi-variational inequalities

Song W.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 4

401-417

First we establish a general existence theorem for a generalized vector qusi-variational inequality in a topological vector space by using a set-valued and vector generalization of Ky Fan minimax principle. As applications, several existence theorems for generalized vector quasi-variational inequalities are derived under assumptions of order-lower (order-upper) semicontinuity or monotonicity of set-valued mappings.