Fixed point theorems by altering distances between the points

Abstract

In this paper we have established some fixed point theorems in complete and compact metric spaces.

Common fixed point theorems for weakly C-contractive mappings in ordered partial metric spaces

“…In this section, we begin with the following definitions( see, e.g., [7,21,25] and references therein). …”

Common Fixed Point Theorems by Altering the Distances Between the Points in Bounded Complete Metric Spaces

“…The purpose of this section is to generalize Theorem 4 of the paper [4] Without loss of generality, we may assume that tn ^ 0 for every integer n. In this case, it is easy to see that the sequence ((f>(tn)) is decreasing and therefore it converges. Since X is compact, we may find a subsequence (x2n(k))k converging to some element z 6 X.…”

“…In the paper [4], the authors gave some fixed point theorems generalizing and unifying many fixed point theorems obtained by Delbosco In this note we work in a bounded complete metric space (X, d). In the second section we prove some common fixed point theorems for sets of self-mappings verifying contractive conditions close to the relation (K) but using only continuous functions <p satisfying (P 2 )-Thus, in this case the assumption u <j> is increasing" becomes superfluous and can be removed.…”

“…Furthermore, our main theorem is an improvement upon some other fixed point theorems (see [3], [5], [6], [7]). In section 3, we establish a common fixed point theorem in compact metric spaces generalizing Theorem 4 of the paper [4] which itself was considered by the authors as a generalization of a theorem given by B. Fisher in [3].…”

Fixed point and multidimensional fixed point theorems with applications to nonlinear matrix equations in terms of weak altering distance functions

“…In the recent years, many authors extended fixed point results for weak contractions and generalized contractions, which are generalizations of Banach contraction mapping principle to partially ordered metric spaces (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]). Some of the above results involve altering distance functions presented by Khan et al in [16]. Now, we recall the definition of an altering distance function.…”