Author:
Guan Hongyan,Gou Jinze,Hao Yan
Abstract
<abstract><p>In the article, we considered the fixed point problem for contractive mappings of integral type in the setting of $ b $-metric spaces for the first time. First, we introduced the concepts of $ \theta $-weak contraction and $ \theta $-$ \psi $-weak contraction. Second, the existence and uniqueness of fixed points of contractive mappings of integral type in $ b $-metric spaces were studied. Meanwhile, two examples were given to prove the feasibility of our results. As an application, we proved the solvability of a functional equation arising in dynamic programming.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference25 articles.
1. S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3 (1922), 51–57. https://doi.org/10.4064/fm-3-1-133-181
2. S. Czerwik, Contraction mappings in $b$-metric spaces, Acta. Math. Inform. Univ. Ostrav., 1 (1993), 5–11.
3. S. Hussain, M. Sarwar, Y. Li, $n$-tupled fixed point results with rational type contraction in $b$-metric spaces, Eur. J. Pure Appl. Math., 11 (2018), 331–351. https://doi.org/10.29020/nybg.ejpam.v11i2.3136
4. W. Shatanawi, A. Pitea, R. Lazovic, Contraction conditions using comparison functions on $b$-metric spaces, Fixed Point Theory A., 2014 (2014). https://doi.org/10.1186/1687-1812-2014-135
5. M. Abbas, J. R. Roshan, S. Sedghi, Common fixed point of four maps in $b$-metric spaces, Hacet. J. Math. Stat., 43 (2014), 613–624.