Best proximity point results in b-metric space and application to nonlinear fractional differential equation

Hussain A., Kanwal T., Adeel M., Radenovic S.

Mathematics, vol.6, no.11, 2018 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 11
  • Publication Date: 2018
  • Doi Number: 10.3390/math6110221
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: B-metric space, Caputo derivative, Suzuki-contraction
  • Uşak University Affiliated: No

Abstract

Based on the concepts of contractive conditions due to Suzuki (Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, 2008, 136, 1861-1869) and Jleli (Jleli, M., Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014, 2014, 38), our aim is to combine the aforementioned concepts in more general way for set valued and single valued mappings and to prove the existence of best proximity point results in the context of b-metric spaces. Endowing the concept of graph with b-metric space, we present some best proximity point results. Some concrete examples are presented to illustrate the obtained results. Moreover, we prove the existence of the solution of nonlinear fractional differential equation involving Caputo derivative. Presented results not only unify but also generalize several existing results on the topic in the corresponding literature.