On -Tupled Coincidence Point Results in Metric Spaces

Abstract

We prove somen-tupled coincidence point results whenevernis even. We give here several new definitions liken-tupled fixed point,n-tupled coincidence point, and so forth. The main result is supported with the aid of an illustrative example.

Erratum to: Generalized n-tupled fixed point theorems for nonlinear contractions

“…That is, our results are true merely for even natural numbers but not for an arbitrary natural number as noted in [1]. (ii) At page 447, line 8:…”

COMMON n-TUPLED FIXED POINT FOR HYBRID PAIR OF MAPPINGS UNDER NEW CONTRACTIVE CONDITION

“…Imdad, Soliman, Choudhury and Das [5] introduced the concept of n−tupled fixed point, n−tupled coincidence point and proved some n−tupled coincidence point and n−tupled fixed point results for single valued mapping.…”

Shorter proofs of some recent even-tupled coincidence theorems for weak contractions in ordered metric spaces

“…. Â X of n identical copies of X: Definition 2.8 ( [13]) Let ðX; "Þ be an ordered set and F : X n ! X and g : X !…”

“…:::; x n 1 Þ: For g ¼ I (identity mapping), Definition 2.8 reduces to mixed monotone property (for details see [13]). …”

“…Here it can be pointed out that the notion of tripled fixed point due to Berinde and Borcut [4] is different from the one defined by Samet and Vetro [32] for n ¼ 3 in the case of ordered metric spaces in order to keep the mixed monotone property working. Recently, Imdad et al [13] extended the idea of mixed gmonotone property to the mapping F : X n ! X (where n is even natural number)and proved an even-tupled coincidence point theorem for nonlinear contraction mappings satisfying mixed g-monotone property.…”