Open AccessAn extension of Karapinar and Sadaranganis’ result through the C-class functions by using α-admissible mapping with applications
Author(s) -
Sudipta Kumar Ghosh,
C. Nahak
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2103973g
Subject(s) - mathematics , extension (predicate logic) , class (philosophy) , contraction (grammar) , fixed point , ordinary differential equation , contraction mapping , type (biology) , pure mathematics , differential equation , algebra over a field , discrete mathematics , mathematical analysis , computer science , artificial intelligence , ecology , biology , medicine , programming language
The main objective of this work is to introduce a new type of non-linear contraction via C-class functions by using ?-admissible mapping. Our new results extend and generalize the very recent results of Karapinar and Sadarangani (2015. RACSAM. [37]). Illustrative examples are given to support our new findings. We have shown that our results satisfy the periodic fixed point results after modifying the contraction. Next, we extend our main findings from a self-mapping T to two self-mappings T; S. Also, an example is provided to justify the effectiveness of our new result on two self mappings, where the partially ordered structure fails. Finally, we apply our new findings to solve ordinary differential and non-linear integral equations.