Dotson\u27s convexity, Banach operator pair and best simultaneous approximations

The existence of common fixed points is established for three mappings where T is either generalized (f,g)-nonexpansive or asymptotically (f,g)-nonexpansive on a set of fixed points which is not necessarily starshaped. As applications, the invariant best simultaneous approximation results are proved

Fixed Point Theorems for Generalized Mizoguchi-Takahashi Graphic Contractions

Remarkable feature of contractions is associated with the concept Mizoguchi-Takahashi function. For the purpose of extension and modification of classical ideas related with Mizoguchi-Takahashi contraction, we define generalized Mizoguchi-Takahashi G-contractions and establish some generalized fixed point theorems regarding these contractions in this paper. Some applications to the construction of a fixed point of multivalued mappings in ε-chainable metric space are also discussed

The Existence of Fixed Point Theorems via -Distance and -Admissible Mappings and Applications

We introduce the concept of the generalized -contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of -distance and -admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature

A Generalization of a Greguš Fixed Point Theorem in Metric Spaces

We first introduce a new class of contractive mappings in the setting of metric spaces and then we present certain Greguš type fixed point theorems for such mappings. As an application, we derive certain Greguš type common fixed theorems. Our results extend Greguš fixed point theorem in metric spaces and generalize and unify some related results in the literature. An example is also given to support our main result

Tripled coincidence and common fixed point results for two pairs of hybrid mappings

The tripled fixed point is a generalization of the well-known concept of “coupled fixed point.” In this paper, tripled coincidence and common fixed point results for two hybrid pairs consisting of multivalued and single valued mappings on a metric space are proved. We give examples to illustrate our results. In the process, several comparable coincidence and fixed point results in the existing literature are improved, unified, and generalized.http://www.hindawi.com/journals/aaa/am201

F-closed sets and coupled fixed point theorems without the mixed monotone property

In this paper we present the notion of F-closed set (which is weaker than the concept of F-invariant set introduced in Samet and Vetro (Ann. Funct. Anal. 1:46-56, 2010), and we prove some coupled fixed point theorems without the condition of mixed monotone property. Furthermore, we interpret the transitive property as a partial preorder and, then, some results in that paper and in Sintunavarat et al. (Fixed Point Theory Appl. 2012:170, 2012) can be reduced to the unidimensional case