Muhammad Sarwar, Abdullah, and Aiman Mukheimer. Fixed Point Result Via Generalized Non-Linear Contraction with Applications. Dynamic Systems and Applications 30 (2021) No.2, 251-262
https://doi.org/10.46719/dsa20213026
ABSTRACT.
In this manuscript, using some new non-linear contractive conditions with an integral power we establish a unique fixed point result in the setting of Gb -metric spaces. We provide an example where main theorem is applicable but most relevant current results in literature fail to have fixed point. We also give an existence result for the system of integral equations. The results established in this manuscript dominant the recent related results in the current literature.
AMS (MOS) Subject Classification. Primary 47H10; secondary 54H25.
Key Words and Phrases. Complete $G_b$-metric space, Cauchy sequence, non-linear contraction, system of integral equation, unique common fixed point.