In this paper,there are   new considerations about the dual of a modular spaces and weak convergence. Two common fixed point theorems for a -non-expansive mapping defined on a star-shaped weakly compact subset are proved,  Here the conditions of affineness, demi-closedness and Opial's property play an active role in the proving our results.

  In this paper, the concept of contraction mapping on a -metric space is extended with a consideration on local contraction.  As a result, two fixed point theorems were proved for contraction on a closed ball in a complete -metric space.

R. Vasuki [1] proved fixed point theorems for expansive mappings in Menger spaces. R. Gujetiya and et al [2] presented an extension of the main result of Vasuki, for four expansive mappings in Menger space. In this article, an important lemma is given to prove that the iteration sequence is Cauchy under suitable condition in Menger probabilistic G-metric space (shortly, MPGM-space). And then, used to obtain three common fixed point theorems for expansive type mappings.

     The aim of this paper is to study the convergence of an iteration scheme for multi-valued mappings which defined on a subset of a complete convex real modular. There are two main results, in the first result, we show that the convergence with respect to a multi-valued contraction mapping to a fixed point. And, in the second result, we deal with two different schemes for two multivalued  mappings (one of them is a contraction and other has a fixed point) and then we show that the limit point of these two schemes is the same. Moreover, this limit will be the common fixed point the two mappings.

In this article, the partially ordered relation is constructed in geodesic spaces by betweeness property, A monotone sequence is generated in the domain of monotone inward mapping,  a monotone inward contraction mapping is a  monotone Caristi inward mapping is proved, the general fixed points for such mapping is discussed and A mutlivalued version of these results is also introduced.

  In this paper, the concept of normalized duality mapping has introduced in real convex modular spaces. Then, some of its properties have shown which allow dealing with results related to the concept of uniformly smooth convex real modular spaces. For multivalued mappings defined on these spaces, the convergence of a two-step type iterative sequence to a fixed point is proved

                 In this paper, we proved coincidence points theorems for two pairs mappings which are defined on nonempty subset   in metric spaces by using condition (1.1). As application, we established a unique common fixed points theorems for these mappings by using the concept weakly compatible (R-weakly commuting) between these mappings.

The study of fixed points on the  maps fulfilling certain contraction requirements has several applications and has been the focus of numerous research endeavors. On the other hand, as an extension of the idea of the best approximation, the best proximity point (ƁƤƤ) emerges. The best approximation theorem ensures the existence of an approximate solution; the best proximity point theorem is considered for addressing the problem in order to arrive at an optimum approximate solution. This paper introduces a new kind of proximal contraction mapping and establishes the best proximity point theorem for such mapping in fuzzy normed space ( space). In the beginning, the concept of the best proximity point was introduced. The concept of prox

The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.