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Fixed point theorems for set-valued G-contractions in a graphical convex metric space with applications

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Abstract

In this paper, we first introduce the concept of graphical convex metric spaces and some basic properties of the underlying spaces. Different from related literature, we generalize Mann iterative scheme and Agrawal iterative scheme for set-valued mappings to above spaces by introducing the concepts of T-Mann sequences and T-Agrawal sequences. Furthermore, by using the iterative techniques and graph theory, we investigate the existence and uniqueness of fixed points for set-valued G-contractions in a graphical convex metric space. Moreover, we present some notions of well-posedness and G-Mann stability of the fixed point problems in the above space. Additionally, as an application of our main results, we discuss the well-posedness and G-Mann stability of the fixed point problems for set-valued G-contractions in a graphical convex metric space.

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Acknowledgements

This research was funded by Training Program for Youth Innovation Talents of Heilongjiang Educational Committee under Grant UNPYSCT-2017078, Postdoctoral Science Foundation of Heilongjiang Province under Grant LBH-Q18067, the Introduction and Cultivation Project of Young and Innovative Talents in Universities of Shandong Province, Nature Science Foundation of Heibei Province under Grant A2019404009 and Postdoctoral Foundation of Heibei Province under Grant B2019003016.

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Correspondence to Ni Yang.

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Chen, L., Yang, N., Zhao, Y. et al. Fixed point theorems for set-valued G-contractions in a graphical convex metric space with applications. J. Fixed Point Theory Appl. 22, 88 (2020). https://doi.org/10.1007/s11784-020-00828-y

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