Mazhar Mehmood, Shaif Saleh Alshoraify, Abdullah Shoaib, and Muhammd Arshad. Fixed Point Results For F-μs -ρ*s Contraction in Quasi b -Metric Spaces With Some Applications. Dynamic Systems and Applications 30 (2021) No.2, 157-183
https://doi.org/10.46719/dsa20213021
ABSTRACT.
In this article, we discuss a recent generalization of a quasi metric space and introduce $F-\mu_{s}-\rho _{s}^{\ast}$ contraction which is a generalization of many recently announced contractions. Fixed point results for some of such contractions have been obtained. An example of our main result is also given which shows that how our result can be used when others fail. We achieve results endowed with a graph. Results in ordered left K-sequentially complete quasi b-metric space have been established. We consider applications of our main results for the existence of a unique common solution for a system of integral equations and of a unique solution for functional equations that arises in dynamic programming.
AMS (MOS) Subject Classification. 47H10; 54H25.
Keywords and Phrases: Common fixed point; multivalued mapping; $\{TS(x_{n})\}$ sequence; $F-\mu _{s}-\rho _{s}^{\ast }-$contraction; complete quasi b-metric space; open ball; graph; partial order; integral equations; dynamic programming.