p ≥2 -cyclic and contractive self-mappings on a set of subsets of a metric space which are simultaneously accretive on the wholemetric space are investigated. The joint fulfilment of the p-cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self-mappings in order to be Kannan self-mappings. The existence and uniqueness of best proximity p...

B. Damjanovi? and D. Dori?, Multivalued generalizations of the Kannan fixed point theorem, Filomat , vol. 25 (1) , DOI: 10. 2298/FIL 1101125D, (2011), 125-131. B. E. Rhoades and M. Abbas, Maps satisfying generalized contractive condition of integral type for which F(T) = F(Tn), International Journal of Pure and Applied Mathematics, vol. 45, no. 2 (2008), 225-231. D. Dori? and R. Lazovi?, Some S...

There exists extensive literature on fixed points of self-mappings in metric and Banach spaces. But in many applications the mappings under examination may not always be self-mappings, therefore fixed point theorems for nonself-mappings form a natural subject for investigation. Assad and Kirk [2] initiated the study of fixed point of nonselfmappings in metrically convex spaces. Indeed while doi...

We give some extensions of the beautiful 1968 fixed point theorem Maia [Maia, M. G. Un’osservazione sulle contrazioni metriche. (Italian) Rend. Sem. Mat. Univ. Padova 40 (1968), 139–143] to three classes enriched contractive mappings in Banach spaces: contractions, Kannan contractions and Ćirić-Reich-Rus contractions.

The study of fixed points of single-valued self-mappings or multivalued self-mappings satisfying certain contraction conditions has a great majority of results inmetric fixed point theory. All these results are mainly generalizations of Banach contraction principle. The Banach contraction principle guarantees the existence and uniqueness of fixed points of certain self-maps in complete metric s...

In this paper we present fixed point results for generalized α-ψ-contractive type mappings in dislocated metric spaces. We also provide some examples to illustrate our results. References 1. Banach S., “Surles operations dans les ensembles abstraites et leurs applications”, Fund. Math., 3 (1922), 133-187. 2. Kannan R., “Some results on fixed points”, Bull. Cal. Math. Soc., 60 (1968), 71-76. 3. ...

In this paper, the concept of cyclic (φ− ψ)-Kannan and cyclic (φ− ψ)-Chatterjea contractions, and fixed point theorems for these types of mappings in the context of complete metric spaces have been introduced. The results proved here extend some fixed point theorems in the literature.