Search

In this paper, we introduce graphic contraction mappings in b-metric spaces and establish some fixed point theorems in the aforesaid space. Appropriate graphs are presented to visualize related definitions and concepts. On the other hand, some examples are presented to verify the authenticity and effectiveness of the established results. Our results generalize and extend some pioneer results existing in the literature. Moreover, applications to existence of solution for ordinary differential equations and for integral equations are also established to show the adequacy of our results. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point results for fuzzy mappings in a complete dislocated b-metric space. Our results generalize and extend the results of Joseph et al. (SpringerPlus 5:Article ID 217, 2016). We also give examples to support our results, and applications relating the results to a fixed point for multivalued mappings and fuzzy mappings are studied. [ABSTRACT FROM AUTHOR]

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate some fixed-point theorems in modular metric spaces. [ABSTRACT FROM AUTHOR]

We introduce the notion of a modified α- ϕ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. The theorems presented provide a generalization of some interesting results in the literature. Two examples and an application to integral equations are given to illustrate the usability of our theory. [ABSTRACT FROM AUTHOR]

In this paper, we prove common coupled fixed point theorems under a Geraghty-type condition using monotone instead of the often used mixed monotone property. Also we give some sufficient conditions for the uniqueness of a common coupled fixed point. An example illustrating our results is provided. [ABSTRACT FROM AUTHOR]

In this paper we consider some new definitions about quadrupled fixed point in abstract metric spaces and obtain some new fixed point results in this field. These results unify, extend and generalize well-known comparable results in the existing literature. We also provide some examples and applications to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new hybrid iterative scheme for finding a common element of the set of zeroes of a maximal monotone operator, the set of fixed points of a relatively quasi-nonexpansive mapping, the sets of solutions of an equilibrium problem and the variational inequality problem in Banach spaces. As applications, we apply our results to obtain strong convergence theorems for a maximal monotone operator and quasi-nonexpansive mappings in Hilbert spaces and we consider a problem of finding a minimizer of a convex function. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an iterative scheme based on a viscosity approximation method with a modified extragradient method for finding a common solutions of a general system of variational inequalities for two inverse-strongly accretive operator and solutions of fixed point problems involving the nonexpansive mapping in Banach spaces. Consequently, we obtain new strong convergence theorems in the frame work of Banach spaces. Our results extend and improve the recent results of Qin et al. (J Comput Appl Math 233:231-240, 2009) and many others. [ABSTRACT FROM AUTHOR]