Some cyclic fixed point results for contractive mappings

Abstract

In this paper, we obtained some new cyclic type fixed point theorems using C-class functions in the framework of metric spaces. Our results extend, generalize, improve and enrich some recent results in the existing literature.

Some new results on (s,q)-Dass-Gupta-Jaggi type contractive mappings in b-metric-like spaces

“…Similarly, in Example 6 we get again the same form N (0, 0) = max 0 0 , 0 =?. The main motivation for our second new result are recent announced papers [33]- [37]. Now, we can prove this significant and important new result which complements and give complete new observations for cyclic type mappings (for more details see [26]).…”

“…each partial b-metric space, is a b-metric-like space, while the converse is not true. For more such examples and details see [4]- [7], [15], [17]- [20], [27], [29]- [37], [40]- [42], [49], [50] and [52].…”

On Coupled Best Proximity Points in Reflexive Banach Spaces

“…In this context, the notions of coupled fixed points [5] and coupled best proximity points for an ordered pair (F, G), F : A × A → B, G : B × B → A, where A, B ⊂ X [6,7] are relevant. Deep results in the theory of coupled fixed points, for example, can be found in [2,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Best Proximity Point Theorems on Rectangular Metric Spaces Endowed with a Graph

“…Over the last decades, many researchers have focused on fixed point theory since it plays a very important role in the resolution of several mathematical models in various fields, see References [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. One of the tools used is the well-known Banach contraction principle, which states that if (X, d) is a complete metric space and f : X −→ X is a contraction self-mapping, then f has a unique fixed point in X.…”