Sentence examples for mappings for problem from inspiring English sources

This section is devoted to an investigation of the Hölder behavior of the perturbed optimal value mappings for problem (2.1).

Considerable effort in the development of a fixed point theory for nonexpansive mappings, mainly for Problem 1.3, has been done in the last 40 years.

The quantitative analysis of various optimal value mappings and optimal solution mappings for optimization problems is an interesting and important topic in optimization theories and applications.

It is well known that many nonlinear problems can be reduced to the search for fixed points of nonexpansive mappings, for example, equilibrium problems, saddle point problems, and variational inequalities.

One of the important topics in optimization theory is the stability analysis of the solution mappings for vector equilibrium problems.

Subsequently, his result was generalized by Aoki [3] for additive mappings and by Rassias [4] for linear mappings, for considering the stability problem with unbounded Cauchy differences.

In this paper, motivated and inspired by the above research results, we introduce a new iterative process with a countable family of nonexpansive mappings for the variational inequality problem in Hilbert spaces.

This problem is connected with the fixed point problem for nonlinear mappings, the problem of finding a zero point of an accretive operator and so on.

The lower semicontinuity of the (weak) efficient solution mappings for parametric vector equilibrium problems under more weaker assumptions is established.

The stability analysis of solution mappings for vector variational inequality problems is an important topic in optimization theory and applications.

Zhang et al. obtained the lower semicontinuity of solution mappings for parametric vector equilibrium problems under the Höder-related assumptions [15].