APPROXIMATE FIXED POINT THEOREMS FOR PARTIAL GENERALIZED CONVEX CONTRACTION MAPPINGS IN $\alpha$-COMPLETE METRIC SPACES

Some approximate fixed point theorems without continuity of the operator using auxiliary functions

“…Some examples are also provided to illustrate the main results and to show the usability of the given hypotheses. These results extend, unify and generalize the main results of Latif et al [11] and of Miandaragh et al [12].…”

“…They have also proved some approximate fixed point theorems for continuous mappings satisfying such contractive conditions in complete metric spaces. The results of Miandaragh et al (see [12]) were extended by Latif et al in [11].…”

A generalization of Istrățescu’s fixed point theorem for convex contractions

“…M. A. Miandaragh, M. Postolache and S. Rezapour [16] introduced the concept of generalized convex contraction and proved some theorems about approximate fixed points of these contractions. Extending these results, A. Latif, W. Sintunavarat and A. Ninsri [12] introduced a new concept called partial generalized convex contraction and established some approximate fixed point results for such mappings in α-complete metric spaces. For more results along these lines of generalization one can also see [10].…”

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].…”