Coincidence and fixed points of non-expansive type mappings on 2-metric spaces

Abstract

In this paper a unique coincidence value is obtained for a class of self mappings satisfying non-expansive type condition on 2-metric spaces under various conditions and a fixed point theorem is also obtained. Mathematics Subject Classification: 54H25

Fixed Point Theorems for Non-compatible, Discontinuous Hybrid Pairs of Mappings on 2-Metric Spaces by Using Implicit Relation

“…It has been introduced by ([3]- [5]) and extensively studied by some mathematicians such as ( [3]- [5]), White [18], [6]. Moreover, a number of authors ( [1], [10], [13], [17]) have studied the contractive, nonexpansive and contraction type mapping in 2-metric spaces. On the other hand, Jungck [7] studied the common fixed points of commuting maps.…”

Implicit Contractive Maps in Ordered Metric Spaces

“…An early construction of this type was proposed in 1963 by Gaehler [12]; the resulting map B : X × X × X → R + was referred to as a 2-metric on X. Short after, this structure was intensively used in many fixed point theorems, under the model in Namdeo et al [26], Negoescu [27] and others; see also Ashraf [2, Ch 3], for a consistent references list. However, it must be noted that this 2-metric is not a true generalization of an ordinary metric; for -as shown in Ha et al [13] -the associated real function B(., ., .)…”

Fixed Point Theorems in 2-Metric Space for Some Contractive Conditions

“…After Gahler there was a flood of new results obtained by many authors in these spaces [4][5][6][7][8]. Military applications of fixed point theory in 2-metric spaces can be found, as well as applications in Medicine and Economics [9][10][11].…”