On combinational contractions with applications.

The aim of this paper is to provide a new hybrid contraction that is a combination of Jaggi, Meir-Keeler and Zamfirescu-type contractions in the framework of a complete metric space. The existence and uniqueness conditions of a fixed point of such contractions are investigated. An example is constructed to demonstrate the validity of the obtained results.

Hybrid fixed point theorems of graphic contractions with applications.

In this work, a family of hybrid contractions, termed Jaggi-type hybrid (ℵ-)-contractive mapping is proposed in metric space equipped with a graph and new conditions under which the mapping is a Picard operator are studied. The novel ideas proposed in this manuscript are exemplified to display the validity of the presented results and to show how they differ from the existing ones. Additionally, some corollaries which reduce our proposed notion to some recently announced concepts in the existing findings are indicated and examined.