Solving split equality fixed point problem of generalized demimetric mapping and certain optimization problem via dynamic step-size technique

Abstract

In this article, we study the split equality problem of certain optimization problem in real Hilbert spaces. We propose a new viscosity iterative algorithm for approximating solution for finite families of split equality variational inequality and split equality fixed point problems of generalized demi metric mapping in real Hilbert spaces. Using our iterative method, we establish a strong convergence result for finding a common element for finite families of variational inequality and fixed point problems of generalized demimetric mapping. We present some consequences and application to the convex minimization problem to validate our main result. Our result complements and generalizes some related results in literature.