TY  - JOUR
T1  - On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces with an Application
AU  - Öztürk, Mahpeyker
AU  - Büyükkaya, Abdurrahman
PY  - 2024
DA  - March
Y2  - 2024
DO  - 10.33434/cams.1414411
JF  - Communications in Advanced Mathematical Sciences
PB  - Emrah Evren KARA
WT  - DergiPark
SN  - 2651-4001
SP  - 27
EP  - 41
VL  - 7
IS  - 1
LA  - en
AB  - In this paper, by taking ${{\mathcal C}_\mathcal{A}}-$simulation function and Proinov type function into account, we set up a new contraction mapping called Suzuki$-$Proinov $\mathpzc{Z^*}_{\aE^*}^{\aR}(\alpha)-$contraction, including both rational expressions that possess quadratic terms and $\aE-$type contractions. Furthermore, we demonstrate a common fixed point theorem through the mappings endowed with triangular $\alpha-$admissibility in the setting of modular $b-$metric spaces. Besides that, we achieve some new outcomes that contribute to the current ones in the literature through the main theorem, and, as an application, we examine the existence of solutions to a class of functional equations emerging in dynamic programming.
KW  - Common fixed point
KW  - Dynamic programming
KW  - Modular $b-$metric space
KW  - Proinov type mappings
KW  - Simulation functions
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UR  - https://doi.org/10.33434/cams.1414411
L1  - https://dergipark.org.tr/en/download/article-file/3638419
ER  -