On almost contractions in partially ordered metric spaces via implicit relations

Abstract

In this paper, we prove general fixed point theorems for self-maps of a partially ordered complete metric space which satisfy an implicit type relation. Our method relies on constructive arguments involving Picard type iteration processes and our uniqueness result uses comparability arguments. Our results generalize a multitude of fixed point theorems in the literature to the context of partially ordered metric spaces.

Unified Fixed Point Theorems via Common Limit Range Property in Modified Intuitionistic Fuzzy Metric Spaces

“…For an extensive collection of implicit relations on different settings, we refer to [41][42][43][44][45].…”

Ordered Vectorial Quasi and Almost Contractions on Ordered Vector Metric Spaces

“…They presented some fixed point results for nondecreasing, nonincreasing and even not monotone contractions. After that, many fixed point results have been given on partially ordered metric spaces, such as [13]. While in [14,15], the notion of partial metric is combined with partial ordering, in [16], the notion of M-metric is combined with partial ordering.…”

Cyclic Contractions and Related Fixed Point Theorems on G-Metric Spaces

“…The theoretical studies are advancing in two main directions: one of them is related with the attempts to generalize the contractive conditions on the maps and thus, weaken them; the other with the attempts to generalize the space on which these contractions are defined. Among the results in the first direction one can mention cyclic contractions, almost contractions, non-expansive and expansive maps [3,4,28,29,30,31,32,33,34,37,50]. In the second direction some of the most extensively studied fields are the cone metric spaces, partial metric spaces and G-metric spaces [1,2,6,7,8,9,10,12,15,16,17,20,21,39,40].…”