Discussion on the existence problems of fixed circle in metric spaces

Deepesh Kumar Patel; Bhupeshwar; Dhananjay Gopal

doi:10.5269/bspm.67262

Deepesh Kumar Patel Visvesvaraya National Institute of Technology, Nagpur, India
Bhupeshwar Visvesvaraya National Institute of Technology, Nagpur 440010, India.
Dhananjay Gopal Guru Ghasidas Vishwavidyalaya, Bilaspur 495009, India

Abstract

This paper deals with the problems of the existence of a fixed circle for multivalued mappings. To prove the validity of the postulates, we develop innovative fixed circle theorems in metric spaces by using Caristi's technique and validate them using illustrated instances with geometric explanation. In fact, for multivalued mappings two different versions of the existence theorems on fixed circle are presented.

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