Unified multi-tupled fixed point theorems involving mixed monotone property in ordered metric spaces

• Main Authors: Aftab Alam, Mohammad Imdad, Javid Ali
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2016-12-01
• Series: Cogent Mathematics
• Subjects: $ * $-fixed points; O-continuity; $ * $-compatibility; MCB property
• Online Access: http://dx.doi.org/10.1080/23311835.2016.1248270

In our endeavor to refine and modify the notion of $ \Upsilon $-fixed point, we introduce the notion of $ * $-fixed point wherein $ * $ is a binary operation on $ I_n $. Moreover, we represent the binary operation $ * $ in the form of a matrix so that the notion of $ * $-fixed point becomes relatively more natural and effective (as compared to $ \Upsilon $-fixed point). We utilize the idea of $ * $-fixed point to prove some unified multi-tupled fixed point theorems for Boyd-Wong type nonlinear contractions satisfying generalized mixed monotone property in ordered metric spaces. Our results unify several classical and well-known n-tupled fixed point results(including coupled, tripled and quadrupled ones) of the existing literature.