The Banach contraction principle is one of the pivotal results in the metric fixed-point theory. It is a popular tool for the solution of existence problems in various fields of mathematics. There are several generalizations of the Banach contraction principle in the related literature on the metric fixed-point theory. Ran and Reurings [15] extended the Banach contraction principle in partially...

In this paper, we obtain a common fixed point theorem for four self maps satisfing (ψ-φ) contractive condition of integral type in ordered partial metric spaces.

In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of  rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces...

Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C → C a contractive mapping (or a weakly contractive mapping), and T : C → C a nonexpansive mapping with the fixed point set F (T ) 6= ∅. Let {xn} be generated by a new composite iterative scheme: yn = λnf(xn)+(1−λn)Txn, xn+1 = (1−βn)yn+βnTyn, (n ≥ 0). It is pr...

Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of E, f : C → C a contractive mapping or a weakly contractive mapping , and T : C → C nonexpansive mapping with the fixed point set F T / ∅. Let {xn} be generated by a...

In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive self-maps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to ...

In this paper we introduce the concept of generalized weakly contractiveness for a pair of multivalued mappings in a metric space. We then prove the existence of a common fixed point for such mappings in a complete metric space. Our result generalizes the corresponding results for single valued mappings proved by Zhang and Song [14], as well as those proved by D. Doric [4].