Common fixed point theorems for a pair of countably condensing mappings in ordered banach spaces

Abstract

In this paper some common fixed point theorems for a pair of multivalued weakly isotone mappings on an ordered Banach space are proved

Fixed point results for contractions involving generalized altering distances in ordered metric spaces

“…If R : X X is the identity mapping (Rx = x for all x X), then S and T are weakly increasing with respect to R implies that S and T are weakly increasing mappings. It is noted that the notion of weakly increasing mappings was introduced in [9] (also see [16,29]). …”

“…Recently, there have been so many exciting developments in the field of existence of fixed point in partially ordered sets (see [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and the references cited therein). The first result in this direction was given by Turinici [27], where he extended the Banach contraction principle in partially ordered sets.…”

Common fixed points for multivalued mappings in ordered partial metric space

“…Note that, in particular, single-valued mappings T ; S : X → X are weakly isotone increasing [4] if Sx ≼ T Sx and T x ≼ ST x hold for each x ∈ X. Definition 1.10 An ordered partial metric space is said to have a sequential limit comparison property if for every nondecreasing sequence (nonincreasing sequence) {x n } in X such that x n → x implies that x n ≤ x (x ≤ x n ), respectively.…”

Common fixed point theorems under implicit relations on ordered metric spaces and application to integral equations

“…for all x ∈ X . (3) [15,16,35] The mapping G is said to be F-weakly isotone increasing if for all x ∈ X we have Gx FGx GFGx. (4) [24] The mapping G is said to be F-strictly weakly isotone increasing if, for all…”