In this paper, we establish that every controlled metric space (X, d α ) induces a Hausdorff controlled metric (H α , CLD(X)) on the class of closed subsets of X which is also complete if (X, d α ) is complete. Furthermore, we define multivalued almost F-contractions on Hausdorff controlled metric spaces and prove some fixed point results. MSC: 46T99; 47H10; 54H25

The aim of this paper is to introduce the notions of α-(F , H)-ϕ, ψ and µ-(F , H)-ϕ, ψ contractions and present several coupled fixed point theorems for this type of contractions in the set of ordered metric spaces. Several examples are offered to illustrate the validity of the obtained results. As an application, the existence of a solution of Fredholm nonlinear integral equations are also investigated.

In this paper, we introduce the notion of T-cyclic (α, β)-contraction and give some common fixed point results for this type of contractions. The presented theorems extend, generalize, and improve many existing results in the literature. Several examples and applications to functional equations arising in dynamic programming are also given in order to illustrate the effectiveness of the obtained results. Primary 47H10; secondary 54H25; 65Q20 MSC:

The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and some other authors and to prove some new coupled fixed point theorems for mappings having a mixed monotone property in a complete metric space endowed with a partial order. Our theorems can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

In this paper, we present some fixed point theorems for cyclic admissible generalized contractions involving C-class functions and admissible mappings in metric-like spaces. We obtain some new results which extend and improve many recent results in the literature. In order to illustrate the effectiveness of the obtained results, several examples and applications to functional equations arising in dynamic programming are also given.

The idea of neighborhood systems is induced from the geometric idea of “near,” and it is primitive in the topological structures. Now, the idea of neighborhood systems has been extensively applied in rough set theory. The master contribution of this manuscript is to generate various topologies by means of the concepts of j -adhesion neighborhoods and ideals. Then, we define a new rough set model derived from these topologies and discussed main features. We show that these topologies are finer than those given in the previous ones under arbitrary binary relations. In addition, we elucidate that these topologies are finer than those topologies initiated based on different neighborhoods and ideals under reflexive relations. Several examples are provided to validate that our model is better than the previous ones.

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M ( x , y , t ) ∗ M ( y , z , s ) . We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.

In this paper, we investigate the existence and uniqueness of a fixed point of almost contractions via simulation functions in metric spaces. Moreover, some examples and an application to integral equations are given to support availability of the obtained results.