Paper Information

Journal:   MATHEMATICAL SCIENCES   2018 , Volume 12 , Number 2; Page(s) 111 To 127.

Some applications of fixed point results for generalized two classes of Boyd– Wong’ s F-contraction in partial b-metric spaces

Author(s):  Singh Deepak, Chauhan Varsha, KUMAM POOM*, Joshi Vishal
* Theoretical and Computational Science (TaCS) Center, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
In this paper, we will present some fixed point results for two classes of generalized contractions of Boyd– Wong type in partial b-metric spaces. More precisely, the structure of the paper is the following. In section one, we present some useful notions and results. The aim of section two is to introduce the concepts of Boyd– Wong F-contractions of type A and of type B and establish some new common fixed point results in partial b-metric spaces. We show the validity and superiority of our main results by suitable examples which are visualized by corresponding surfaces and related graphs. In section three, we correct some slip-ups in some recent papers. Finally, in section four, two applications to integral equation and periodic boundary value problem are included which make effective the new concepts and results.
Keyword(s): Common fixed point,Partial metric spaces,b-metric spaces,F-contraction,a-Admissible
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