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Article

Best Proximity Point Results in b-Metric Space and Application to Nonlinear Fractional Differential Equation

1
Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
2
Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(11), 221; https://doi.org/10.3390/math6110221
Received: 1 October 2018 / Revised: 23 October 2018 / Accepted: 24 October 2018 / Published: 28 October 2018
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
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. View Full-Text
Keywords: Suzuki-contraction; b-metric space; Caputo derivative Suzuki-contraction; b-metric space; Caputo derivative
MDPI and ACS Style

Hussain, A.; Kanwal, T.; Adeel, M.; Radenovic, S. Best Proximity Point Results in b-Metric Space and Application to Nonlinear Fractional Differential Equation. Mathematics 2018, 6, 221. https://doi.org/10.3390/math6110221

AMA Style

Hussain A, Kanwal T, Adeel M, Radenovic S. Best Proximity Point Results in b-Metric Space and Application to Nonlinear Fractional Differential Equation. Mathematics. 2018; 6(11):221. https://doi.org/10.3390/math6110221

Chicago/Turabian Style

Hussain, Azhar, Tanzeela Kanwal, Muhammad Adeel, and Stojan Radenovic. 2018. "Best Proximity Point Results in b-Metric Space and Application to Nonlinear Fractional Differential Equation" Mathematics 6, no. 11: 221. https://doi.org/10.3390/math6110221

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