Fixed point theorems for convex contraction mappings on cone metric spaces

Some Fixed Point Theorems for Orbitally-(p, q)-Quasi-contraction Mappings

“…In Section 3, we extend the concept of .p; q/-quasi-contraction mappings [7] in cone metric space. This mapping type extends the Ilić and Rakočević's quasi-contraction mappings, convex contraction mappings of order n (see, for instance, [1,10]) and the two-sided convex contraction mappings [10]. The main result of this section is that every continuous .p; q/-quasi-contraction mapping in complete cone metric space has a unique fixed point and the Piccard iteration converges to this point.…”

F-Convex Contraction via Admissible Mapping and Related Fixed Point Theorems with an Application

“…Further, he showed with example (see Example 1.3, [4]) that T is in the class of convex contraction but it is not a contraction. Recently, some researchers studied on generalization of such class of mappings in the setting of various spaces (for example, Alghamdi et al [5], Ghorbanian et al [6], Latif et al [7], Miandaragh et al [8], Miculescu [9], etc.). Khan et al [10], introduced the notion of generalized convex contraction mapping of type-2 by extending the generalized convex contraction (respectively, generalized convex contraction of order-2) of Miandaragh et al [8] and the convex contraction mapping of type-2 of Istrǎţescu [4].…”

On (α,p)-convex contraction and asymptotic regularity

“…Some works have appeared recently on generalization of such class of mappings in the setting of metric, ordered metric, and cone metric, b-metric and 2-metric spaces (for example, Alghamdi et al [1], Ghorbanian et al [7], Miandaragh et al [14], Miculescu and Mihail [15], Khan et al [12], etc. ).…”