Existence theorems of a new set-valued MT-contraction in <em>b</em>-metric spaces endowed with graphs and applications


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	Existence theorems of a new set-valued MT-contraction in b-metric spaces endowed with graphs and applications


	Fixed Point Theory, Volume 19, No. 2, 2018, 785-800, June 1st, 2018 DOI: 10.24193/fpt-ro.2018.2.58 Authors: Jukrapong Tiammee, Suthep Suantai and Yeol Je Cho Abstract: A new concept of set-valued Mizoguchi-Takahashi G-contractions is introduced in this paper and some fixed point theorems for such mappings in b-metric spaces endowed with directed graphs are established under some sufficient conditions. Our results improve and extend those of [20] and [24]. We also give some examples supporting our main results. As an applications, we prove the existence of fixed points for multivalued mappings satisfying generalized MT-contractive condition in ε-chainable b-metric spaces and the existence of a solution for some integral equations. Key Words and Phrases: Fixed point, Mizoguchi-Takahashi function, b-metric spaces, directed graph, set-valued map, integral equation, ε-chainable metric space. 2010 Mathematics Subject Classification: 47H04, 47H10, 54H25. Published on-line: June 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents