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Notes on multidimensional fixed-point theorems

Akhadkulov H., Noorani S. M., Saaban A. B., Alipiah F. M., Alsamir H.

Demonstratio Mathematica

2017

Vol. 50, nr 1

360--374

In this paper we prove the existence and uniqueness of coincident (fixed) points for nonlinear mappings of any number of arguments under a (ψ ,θ, φ)-weak contraction condition without O-compatibility. The obtained results extend, improve and generalize some well-known results in the literature to be discussed below. Moreover, we present an example to show the efficiency of our results.

Some properties of T-metric spaces and a common fixed point theorem

Sedghi S., Altun I., Shobe N.

Fasciculi Mathematici

2012

Nr 48

105--118

In this paper, we introduce the new definitions of T-metric space and give some properties of it. Also, we prove a common fixed point theorem for for four mappings under the condition of weakly compatible in complete T-metric spaces. A lot of fixed point theorems on ordinary metric space are special case of our main result, since every ordinary metric space is also T-metric space.

Two results on Jachymski-Schörder-Stein contractions

Reich S., Zaslavski A. J.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

Vol. 56, no 1

53-58

We establish two fixed point theorems for certain mappings of contractive type.

Contractive mappings are Kannan mappings, and Kannan mappings are contractive mappings in some sense

Suzuki T.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 1

45--58

In this paper, we prove that a mapping T on a metric space is contractive with respect to a τ-distance if and only if it is Kannan with respect to a τ-distance.