ABSTRACT
The theory of multivalued mappings has been extended by many researchers in different ways. The basic tool for generalization is S. Banach contraction principle which has been used in different ways, either by considering generalized contractive conditions of mappings or extending the area of mappings. Following the Banach contraction principle, the hypothesis of multivalued maps has different applications in convex optimization, dynamical frameworks, commutative polynomial math, differential conditions, and economics. In 2003, W. A. Kirk et al. extended the Banach contraction principle to cyclic contractive mappings, studied the cyclical contractive condition for self-mappings, and proved some fixed point results. The study of the relationship between the convergence of a sequence of mappings and their fixed points, known as the stability of fixed points, has been widely studied in various settings. Multivalued mappings often have more fixed points than their single-valued mappings. Therefore, the set of fixed points of multivalued mappings becomes larger and more interesting for the study of stability.
