Solutions and Ulam-Hyers stability of differential inclusions involving Suzuki type multivalued mappings on b-metric spaces

Abstract

Introduction/purpose: This paper presents coincidence and common fixed points of Suzuki type multivalued operators on b-metric spaces.
 Methods: The limit shadowing property was discussed as well as the well- posedness and the Ulam-Hyers stability of the solution for the fixed point problem of such operators.
 Results: The upper bound of the Hausdorff distance between the fixed point sets is obtained. Some examples are presented to support the obtained results.
 Conclusion: The application of the obtained results establishes the existence of differential inclusion.

Fixed point results for weak contractions in partially ordered b-metric space

“…Thus, for . Hence, equation ( 5 ) becomes Since , then is a Cauchy sequence from [ 1 , 6 , 8 , 18 ]. Also, the completeness of gives that .…”

“…A b -metric space is one of several generalizations of a standard metric space proposed by Bakhtin in his work [ 9 ], and widely used by Czerwik in his work [ 14 , 15 ]. Following that, a lot of progress was made in acquiring the results of fixed points to single valued as well as multi-valued operators in the space, as evidenced by [ 1 , 2 , 4 – 8 , 10 , 13 , 16 – 18 , 20 , 21 , 23 , 24 , 26 , 27 , 31 , 38 – 41 ].…”

Some fixed point results of generalized $$(\phi , \psi )$$-contractive mappings in ordered b-metric spaces

“…This means that for . Hence, we obtain from ( 6 ) that Since, then the sequence is a Cauchy sequence by [ 3 , 5 , 8 , 10 ]. Since P is complete, then there exists some such that .…”

“…One of the most influential generalization is b -metric space also called metric type space by some authors, introduced and studied by Bakhtin [ 1 ] in 1989. later, Czerwik [ 2 ] generalized the Banach contraction principle in the context of complete b -metric spaces. After that many researchers have carried out further studies in b -metric space and their topological properties, some of which are in [ 3 – 18 ] and the references therein.…”

Fixed point results of \((\phi,\psi)\)-weak contractions in ordered \(b\)-metric spaces

“…Later, a series of papers have been dedicated to the improvement of fixed point results for single valued and multi-valued operators on b-metric spaces by following various topological properties, some of such are from [1,3,6,5,9,20,22,28,29,30,32,34,36,39,40,41,43,53].…”