A Fixed Point Approach to the Hyers-Ulam-Rassias Stability Problem of Pexiderized Functional Equation in Modular Spaces

In this paper, we consider pexiderized functional equations for studying their Hyers-Ulam-Rassias stability. This stability has been studied for a variety of mathematical structures. Our framework of discussion is a modular space. We adopt a fixed-point approach to the problem in which we use a generalized contraction mapping principle in modular spaces. The result is illustrated with an example.

On the existence problem for a fixed point of a generalized contracting multivalued mapping

We discuss the still unresolved question, posed in [S. Reich, Some Fixed Point Problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 57:8 (1974), 194–198], of existence in a complete metric space X of a fixed point for a generalized contracting multivalued map Φ: X⇉X having closed values Φ(x)⊂X for all x∈X. Generalized contraction is understood as a natural extension of the Browder–Krasnoselsky definition of this property to multivalued maps: ∀x,u∈X h(φ(x),φ(u))≤ η(ρ(x,u)), where the function η:R_+→R_+ is increasing, right continuous, and for all d>0, η(d)<d (h(•,•) denotes the Hausdorff distance between sets in the space X). We give an outline of the statements obtained in the literature that solve the S. Reich problem with additional requirements on the generalized contraction Φ. In the simplest case, when the multivalued generalized contraction map Φ acts in R, without any additional conditions, we prove the existence of a fixed point for this map.

Fixed Point Theorem for Cyclic Weakly Generalized Contraction Mapping of Ciric Type

In this article, the concept of cyclic weakly generalized contraction mapping of Ciric type has been introduced and the existence of a fixed point for such mappings in the setup of complete metric spaces has been established. Result obtained extends and improves some fixed point results in the literature. Example is also given to show that class of contraction mappings introduced in the paper is strictly larger class than the class of mappings used in the literature and thus ensures wider applicability of the result by producing the solutions to new problems.

Generalized contraction involving an open ball and common fixed point of multivalued mappings in ordered dislocated quasi metric spaces

The aim of this work is to obtain fixed point results for multivalued mappings satisfying generalized contractions on the intersection of an open ball and a sequence in left (right) K-sequentially complete ordered dislocated quasi metric space. An example has been built to demonstrate the novelty of results. Our results generalize and extend the results of Altun et al. (J. Funct. Spaces, Article ID 6759320, 2016)

Unique Common Fixed Point Results with Application in Fuzzy Metric Spaces

Fixed points in fuzzy theory plays a very significant task in the field of mathematical and computer sciences. This theory has numerous applications in the area of communication and technology, computer science and information security and many others. Many researchers established the results of point for an assortment of mappings in different metric spaces. In present paper, our aim is to establish a common fixed point theorem satisfying generalized contraction in FMS. We also bestow an application for integral type contraction

Fixed Point Results for Generalized Contraction Mappings and Cyclical Mappings in b-Metric Spaces Endowed with a Digraph

In this paper, we establish a fixed point theorem for generalized contraction mappings in b-metric spaces endowed with a digraph. As an application of this result, we obtain fixed points of cyclical mappings in the setting of b-metric spaces. Our results extend and generalize several existing results in the literature.

Some Generalized Contraction Classes and Common Fixed Points in b-Metric Space Endowed with a Graph

We have introduced the new notions of R-weakly graph preserving and R-weakly α -admissible pair of multivalued mappings which includes the class of graph preserving mappings, weak graph preserving mappings as well as α -admissible mappings of type S, α * -admissible mappings of type S and α * - orbital admissible mappings of type S respectively. Some generalized contraction and rational contraction classes are also introduced for a pair of multivalued mappings and common fixed point theorems are proved in a b-metric space endowed with a graph. We have also applied our results to obtain common fixed point theorems for R-weakly α -admissible pair of multivalued mappings in a b-metric space which are the proper extension and generalization of many known results. Proper examples are provided in support of our results. Our main results and its consequences improve, generalize and extend many known fixed point results existing in literature.

New Types of F-Contraction for Multivalued Mappings and Related Fixed Point Results in Abstract Spaces

In this article, we establish fixed point results for a pair of multivalued mappings satisfying generalized contraction on a sequence in dislocated b-quasi metric spaces and Fρs⁎ Khan type contraction on a sequence in b-quasi metric spaces. An example and an application have been discussed. Our results modify and generalize many existing results in literature.