Common fixed point theorems for a mixed family of fuzzy and crisp mappings

Universe as a self‐observable, self‐ethical, life‐embedding mathematical system

“…This is enough to support lower levels of life organization. However, such fixed points can stand for mental images in a space organized as a brain‐type system (Bounias and Bonaly, 1997b; Bounias, 2000, Sharma et al , 2001). This denotes a higher level of organization in which greater levels are required:…”

“…Unicity of fixed points involves compatibility and semi‐compatibility of mappings, which is materialized in biological anatomy by chiasm structures. These conditions allow fixed points to exist also in presence of fuzzy components and discontinuity of some parts (Singh et al , 1997; Sharma et al , 2001).…”

A System of Nonlinear Operator Equations for a Mixed Family of Fuzzy and Crisp Operators in Probabilistic Normed Spaces

“…On the other hand, since then, several kinds of variational inequalities, variational inclusions, complementarity problems, and nonlinear equations with fuzzy mappings were Journal of Inequalities and Applications introduced and studied by many authors see, e.g., [8][9][10][11][12][13][14][15] . Sharma et al 15 considered two nonfuzzy mappings and a sequence of fuzzy mappings to define a hybrid D-compatible condition.…”

“…Sharma et al 15 considered two nonfuzzy mappings and a sequence of fuzzy mappings to define a hybrid D-compatible condition. They also showed the existence of common fixed points under such condition, where the range of the one of the two nonfuzzy mappings is joint orbitally complete.…”