for all x, y ∈ X. Kannan [] proved that if X is complete, then a Kannan mapping has a fixed point. It is interesting that Kannan’s theorem is independent of the Banach contraction principle []. Also, Kannan’s fixed point theorem is very important because Subrahmanyam [] proved that Kannan’s theorem characterizes the metric completeness. That is, a metric space X is complete if and only if ev...

In this paper, we first introduce a new family of functions like an implicit function called ?-functions. Furthermore, concept ?-?F-fuzzy contractive mappings, which is weaker than the class fuzzy F-contractive mappings. Then, existence and uniqueness fixed point are established for type mappings in setting metric spaces. Moreover, some examples application to nonlinear fractional differential ...

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study...

In this paper, we present some new and novel mappings defined over 0,1 with the help of GA-convex functions. As a consequence, obtain companions Fejér-type inequalities for functions these mappings, which provide refinements known results. The properties are discussed as well.

In the piece of this note, we mention various Suzuki-type fuzzy contractive inequalities in 1-Z-complete metric-like spaces for uniqueness and existence a fixed point prove few theorems, which are appropriate generalizations some latest famed results literature. Mainly, generalize Θ-contraction terms also ϓ-contractive mapping view Suzuki-type. For new group functions, acceptable conditions for...

* Correspondence: [email protected]. edu.tw Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan Full list of author information is available at the end of the article Abstract In this paper, we introduced two new classes of nonlinear mappings in Hilbert spaces. These two classes of nonlinear mappings contain some important classes of nonlinear mappings, l...

* Correspondence: [email protected] Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran Full list of author information is available at the end of the article Abstract In this paper, the existence of a fixed point for TF-contractive mappings on complete metric spaces and cone metric spaces is proved, where T : X ® X is a one to one and closed graph...