Fixed points and best proximity points for some general classes of multi-valued operators

Abstract

In this paper, suggested by several concepts of multi-valued Feng–Liu operators, we will consider a general abstract class of operators and we will give some stability properties for special subclasses of it. The general results presented here cover several existence and stability theorems in the recent literature. An application to thhe best proximity point theory is also given.

Keywords:

• Complete metric space
• multi-valued operator
• fixed point
• contraction type operator
• stability properties

2010 Mathematics Subject Classifications:

• 47H10
• 47N20
• 54H25

Acknowledgments

The first two authors are grateful to Professor Jen-Chih Yao and the Department of Mathematics for the kind hospitality and support during the research stage at NSYSU Kaohsiung, Taiwan. All authors have equal contributions to all phases of the work: investigation, conceptualization and writing. All authors have read and agreed to the published version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first two authors welcome the support of the Babeş-Bolyai Development Fund 2023.