In this paper, we give a fixed point theorem for $(psi,varphi)$-weakly contractive mappings in complete $b$-metric spaces. We also give a common fixed point theorem for such mappings in complete $b$-metric spaces via altering functions. The given results generalize two known results in the setting of metric spaces. Two examples are given to verify the given results.

Endpoint results are presented for multi-valued cyclic contraction mappings on complete metric spaces (X, d). Our results extend previous results given by Nadler (1969), Daffer-Kaneko (1995), Harandi (2010), Moradi and Kojasteh (2012) and Karapinar (2011).

In this paper, we introduce a new class of set-valued contractions and obtain a xed point theoremfor such mappings in complete metric spaces. Our main result generalizes and improves many well-known xed point theorems in the literature.

In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

In this article, we define the vector valued multiple of $chi^{2}$ over $p$-metric sequence spaces defined by Musielak and study some of their topological properties and some inclusion results.

In this paper, we extend and improve the condition of contraction of results of Azam et al. for two single-valued mappings on a closed ball in complex valued metric spaces.

*Correspondence: [email protected] 1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China Full list of author information is available at the end of the article Abstract Based on the concept and properties of C∗-algebras, the paper introduces a concept of C∗-algebra-valued b-metric spaces which generalizes the concept of C∗-algebra-valued metric spac...