On a Version of Dontchev and Hager’s Inverse Mapping Theorem

Abstract

By revisiting an open question raised by Kirk and Shahzad, we are able to prove a generalized version of Nadler’s fixed-point theorem in the context of strong b-metric space. Such a result leads us to prove a new version of Dontchev and Hager’s inverse mapping theorem. Some examples are provided to illustrate the results.

Keywords

• strong <i>b</i>-metric space (SbMS)
• Nadler’s fixed-point theorem
• inverse mapping theorem