Caristi-like condition. Existence of solutions to equations and minima of functions in metric spaces


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	Caristi-like condition. Existence of solutions to equations and minima of functions in metric spaces


	Fixed Point Theory, Volume 20, No. 1, 2019, 31-58, February 1st, 2019 DOI: 10.24193/fpt-ro.2019.1.03 Authors: A.V. Arutyunov, B.D. Gel'man, E.S. Zhukovskiy and S.E. Zhukovskiy Abstract: In the paper, there were studied Caristi-like conditions that guaranteed existence of a minimum of a function on a metric space. For functions dependent on a parameter, there were obtained conditions for existence of a minimum for each value of the parameter. These results were applied to derive conditions for fixed point and coincidence point existence for mappings in metric spaces. For mappings dependent on a parameter, there were obtained conditions of coincidence point existence for each value of the parameter. Key Words and Phrases: Caristi-like conditions, coincidence point, fixed point. 2010 Mathematics Subject Classification: 54H25, 49J53, 47H10. Published on-line: February 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents