Search results for " b-metric space"
showing 4 items of 4 documents
Fixed points for multivalued mappings in b-metric spaces
2015
In 2012, Samet et al. introduced the notion ofα-ψ-contractive mapping and gave sufficient conditions for the existence of fixed points for this class of mappings. The purpose of our paper is to study the existence of fixed points for multivalued mappings, under anα-ψ-contractive condition of Ćirić type, in the setting of completeb-metric spaces. An application to integral equation is given.
Fixed point results under generalized c-distance with application to nonlinear fourth-order differential equation
2019
We consider the notion of generalized c-distance in the setting of ordered cone b-metric spaces and obtain some new fixed point results. Our results provide a more general statement, under which can be unified some theorems of the existing literature. In particular, we refer to the results of Sintunavarat et al. [W. Sintunavarat, Y.J. Cho, P. Kumam, Common fixed point theorems for c-distance in ordered cone metric spaces, Comput. Math. Appl. 62 (2011) 1969-1978]. Some examples and an application to nonlinear fourth-order differential equation are given to support the theory.
The Sehgal’s Fixed Point Result in the Framework of ρ-Space
2022
In this paper, we prove a fixed point theorem of Sehgal type (see Sehgal, V.M., Proc Amer Math Soc 23: 631–634, 1969) in a more general setting of ρ-space (see Secelean, N.A. and Wardowski, D., Results Math, 72: 919–935, 2017). In this way, we can find, as particular cases, some results of Sehgal type in metric, b-metric and rectangular b-metric spaces.
Fixed point theorems for α-set-valued quasi-contractions in b-metric spaces
2015
Recently, Samet et al. [B. Samet, C. Vetro and P. Vetro, Fixed point theorems for alpha-psi-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165] introduced the notion of alpha-psi-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notions of alpha-set-valued contraction and alpha-set-valued quasi-contraction and we give some fixed point theorems for such classes of mappings in the setting of b-metric spaces and ordered b-metric spaces. The presented theorems extend, unify and generalize several well-known comparable results in the existing literature.