: At first, we recall the basic concept, By a residual lattice is meant an algebra

In this paper authors have proved some results on Glivenko congruence R with respect to Semi prime ideal J in a nearlattice S. They showed that the quotient nearlattice R S is distributive if and only if J is semiprime. Moreover, they have included a prime separation theorem for semiprime ideals. At the end some results on ⊥ A and 0 A for a 0-distributive nearlattice are given. Finally they have included a characterization of distributive nearlattices with the help of Separation theorems by using semiprime ideals.

A modified general version of Gauss-type proximal point algorithm (GGPPA) is presented in this article for solving the parameterized generalized equation y ∈ F(x), where y is a parameter and a set-valued mapping F: X ⇉ 2Y is acting between two different Banach spaces X and Y. We demonstrate the existence of any sequence produced by the modified GGPPA by taking certain presumptions into account, and we use metrically regular mapping to demonstrate the uniformity of semi-local and local convergence findings. Finally, we present a numerical experiment to verify the uniformity of semi-local convergence result.