Indicator of $S$-Hausdorff metric spaces and coupled strong fixed point theorems for pairwise contraction maps

Subject Areas : Statistics

Ghorban Khalilzadeh Ranjbar ¹ (Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran)
Mohammad Esmael Samei ² (Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran)

Received: 2018-10-22 Accepted : 2020-01-22 Published : 2020-04-01

Keywords: جفت نقاط ثابت قوی, جفت نقاط ثابت, $S$-هاسدورف جزئی, فضای متریک,

Abstract :

In the study of fixed points of an operator it is useful to consider a more general concept, namely coupled fixed point. Edit In this paper, by using notion partial metric, we introduce a metric space $S$-Hausdorff on the set of all close and bounded subset of $X$. Then the fixed point results of multivalued continuous and surjective mappings are presented. Furthermore, we give a positive result on the Nadler contraction theorem for multivalued mappings in this space. In the following, by expressing pseudo-Banach-type pairs of mappings, we study the conditions for the existence of a unique coupled strong fixed point in these mappings. Pseudo-Chatterjae mapping $F:X \times X\to X$ satisfies in \[d\left( F(x, y), F(u, v) \right) \leq k \max \left\{ d\left( x, F(u, v)\right), d\left( F(x, y), u\right) \right\}, \] where $x, v \in A$, $y, u \in B$ and $0 < k < \frac{1}{2}$. Also, We define some quasi-Banach and Pseudo-Chatterjae contraction inequalities. In addition, we will prove theorems about coupled fixed points. Finally, several examples are presented to understand the our results.

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