Okeke Godwin Amechi, Francis Daniel, de la Sen Manuel
Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526 Owerri, Imo State, Nigeria.
Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia) - P.O. Box 644- Bilbao, Barrio Sarriena, 48940- Leioa, Spain.
Heliyon. 2020 Aug 26;6(8):e04785. doi: 10.1016/j.heliyon.2020.e04785. eCollection 2020 Aug.
We prove some theorems on the existence and uniqueness of fixed point for Reich-type contraction mappings and Geraghty-type mappings satisfying rational inequalities in modular metric spaces. Our results include the results of [1] and [2] as special cases. Furthermore, we apply our main results in proving the existence and uniqueness of solution of nonlinear Barbashin-type integrodifferential equation satisfying a given initial value problem in modular metric space .
我们证明了关于模度量空间中满足有理不等式的Reich型压缩映射和Geraghty型映射的不动点存在性和唯一性的一些定理。我们的结果包括文献[1]和[2]的结果作为特殊情况。此外，我们应用主要结果证明了在模度量空间中满足给定初值问题的非线性Barbashin型积分微分方程解的存在性和唯一性。
