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

Abstract

In our endeavor to refine and modify the notion of -fixed point, we introduce the notion of -fixed point wherein is a binary operation on . 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 -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.