Applications of fixed point results for cyclic Boyd-Wong type generalized \(F-\psi\)-contractions to dynamic programming


Deepak Singh - Department of Applied Sciences, NITTTR, Under Ministry of HRD, Govt. of India, Bhopal, (M.P.), 462002 India.
Varsha Chauhan - Department of Mathematics, NRI Institute of Research & Technology, Bhopal M.P, India.
Poom Kumam - KMUTTFixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.
Vishal Joshi - Department of Mathematics, Jabalpur Engineering College, Jabalpur (M.P.), India.
Phatiphat Thounthong - Renewable Energy Research Centre, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand.


Recently, Piri et al. [H. Piri, P. Kumam, Fixed Point Theory Appl., 2014 (2014), 11 pages] refined the result of Wardowski [D. Wardowski, Fixed Point Theory Appl., 2012 (2012), 6 pages] by launching some weaker conditions on the self-map regarding a complete metric space and over the mapping F. In the article, we inaugurate Boyd-Wong type generalized F-\(\psi\)-contraction and prove some new fixed point results in partial metric spaces, also we deduce fixed point results involving cyclic Boyd- Wong type generalized F-\(\psi\)-contraction in the same setup. These results substantially generalize and improve the corresponding theorems contained in Wardowski ([D. Wardowski, Fixed Point Theory Appl., 2012 (2012), 6 pages] [D. Wardowski, N. Van Dung, Demonstr. Math., 47 (2014), 146–155]), Matthews [S. G. Matthews, Papers on general topology and applications, Flushing, NY, (1992), 183–197, Ann. New York Acad. Sci., New York Acad. Sci., New York, 728 (1994)], and others. The paper includes two applications and some illustrative examples to highlight the realized improvements.