Fixed point theorems for g-monotone maps on partially ordered S-metric spaces

Abstract

In this paper, we prove some fixed point theorems for-monotone maps on partially ordered S-metric spaces. Our results generalize fixed point theorems in [1] and [7] for maps on metric spaces to the structure of S-metric spaces. Also, we give examples to demonstrate the validity of the results.

Fixed Points of Generalized (Alpha, Psi,phi)-Contractive Maps and Property(p) in S-Metric Spaces

“…Sedghi, Shobe and Aliouche [19] asserted that S-metric space is a generalization of G-metric space. But, very recently Dung, Hieu and Radojevic [8] have verified by example (Example 2.1 and Example 2.2) that S-metric space is not a generalization of G-metric space or vice versa. Therefore, the classes of Gmetric spaces and S-metric spaces are different.…”

“…Therefore, the classes of Gmetric spaces and S-metric spaces are different. Recent papers dealing with fixed point theorems for mappings satisfying certain contractive conditions on S-metric spaces can be referred in [1,2,8,12,15,16,20]. Now we provide some preliminaries and basic definitions which we use throughout this paper.…”

“…Example 1.2. (Example 1.9 [8]). Let X = R and let S(x, y, z) = |y + z − 2x| + |y − z| for all x, y, z ∈ X.…”

“…Lemma 1.2. [8] Let (X, S) be an S-metric space. Then (i ) S(x, x, z) ≤ 2S(x, x, y) + S(y, y, z) and (ii ) S(x, x, z) ≤ 2S(x, x, y) + S(z, z, y).…”

Best Proximity Points for Monotone Relatively Nonexpansive Mappings in Ordered Banach Spaces

“…Recently, many authors studied the existence of fixed points of monotone nonexpansive mappings defined on partially ordered Banach spaces (see for example [10][11][12][13][14][15]). Recall that a self mapping T on X is said to be monotone nonexpansive if T is monotone and Tx − Ty ≤ x − y , for every comparable elements x and y.…”