(GDDVIP; λ) AND THE VARIABLE STEP ITERATIVE METHOD FOR T-η-INVEX FUNCTION OF ORDER λ IN HILBERT SPACES

Abstract

The aim of this paper is to introduce the concept of generalized dierentialdominated variational inequality problem of order λ> 0 (GDDVIP; λ) and T-η-invex function of order and study them by using a function of proportionality. The problems suchas Minimization Problem with variational inequality condition (MPVIC), and generalizeddierential inequality problem(GDIP) are studied in the presence of T-η-invex function of order λ by using the function of proportionality. The existence of the T-η-invex function oforder λ is studied in Hilbert space by using the variable step iterative method. The iterativeprocess considered in the paper admits the presence of variable iteration parameters, whichcan be useful in numerical implementation to find T-η-invex function of order λ. Finally theexistence theorem of T-η-invex function of order λ is studied with a concrete example.