Well-posed fixed point results and data dependence problems in controlled metric spaces

Abstract

Abstract The present research is aimed to analyze the existence of strict fixed points (SFPs) and fixed points of multivalued generalized contractions on the platform of controlled metric spaces (CMSs). Wardowski-type multivalued nonlinear operators have been introduced employing auxiliary functions, modifying a new contractive requirement form. Well-posedness of obtained fixed point results is also established. Moreover, data dependence result for fixed points is provided. Some supporting examples are also available for better perception. Many existing results in the literature are particular cases of the results established.

Keywords

• Strict fixed points (SFPs)
• Controlled metric spaces (CMSs)
• Well-posedness
• Data dependence result
• Auxiliary functions