Some fixed point theorems for mappings satisfying rational inequality in modular metric spaces with applications

Godwin Amechi Okeke; Daniel Francis; Manuel de la Sen

doi:10.1016/j.heliyon.2020.e04785

Some fixed point theorems for mappings satisfying rational inequality in modular metric spaces with applications

Heliyon. 2020 Aug 26;6(8):e04785. doi: 10.1016/j.heliyon.2020.e04785. eCollection 2020 Aug.

Authors

Godwin Amechi Okeke¹, Daniel Francis¹, Manuel de la Sen²

Affiliations

¹ Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526 Owerri, Imo State, Nigeria.
² 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.

Abstract

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 $X_{ω}$ .

Keywords: Barbashin-type integrodifferential equation; Existence and uniqueness; Fixed point; Modular metric spaces.