Search

The aim of this paper is to define and study the concept of $\mathcal{I}$-convergence in fuzzy cone normed space which is a generalization of R. Saadati and S. M. Vaezpour type fuzzy normal space. We also obtained some basic properties of $\mathcal{I}$-convergence. In fuzzy cone normed space, $\mathcal{I}$-limit point and $\mathcal{I}$-cluster point were defined and studied.

Abstract This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, and fixed point results for set-valued fuzzy cone-contraction and for multi-valued fuzzy cone-contraction mappings. We prove a fixed point theorem for multi-valued rational type fuzzy cone-contractions in fuzzy cone metric spaces. Our results extend and improve some results given in the literature.

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application. [ABSTRACT FROM AUTHOR]

The purpose of this study is to present the idea of an f-partition for a closed interval. Additionally, we introduce a new notion for fuzzy cone metric spaces called a fuzzy cone integrable function and prove fundamental fixed-point theorems. Moreover, we develop the concept of a ξ -fuzzy cone integrable function. Finally, we present new results of the fixed- point theorem for ξ -fuzzy cone integrable functions. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we introduce the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. We establish some coupled fixed point results without the mixed monotone property, and also present some coupled fixed results using the partial order metric in the said space. We present some strong coupled fixed point theorems using cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. Moreover, we present an application of nonlinear integral equations for the existence of a unique solution to support our work.

Abstract In this paper, we present some weakly compatible and quasi-contraction results for self-mappings in fuzzy cone metric spaces and prove some coincidence point and common fixed point theorems in the said space. Moreover, we use two Urysohn type integral equations to get the existence theorem for common solution to support our results. The two Urysohn type integral equations are as follows: x ( l ) = ∫ 0 1 K 1 ( l , v , x ( v ) ) d v + g ( l ) , y ( l ) = ∫ 0 1 K 2 ( l , v , y ( v ) ) d v + g ( l ) , $$\begin{aligned} &x(l)= \int _{0}^{1}K_{1}\bigl(l,v,x(v) \bigr)\,dv+g(l), \\ &y(l)= \int _{0}^{1}K_{2}\bigl(l,v,y(v) \bigr)\,dv+g(l), \end{aligned}$$ where l ∈ [ 0 , 1 ] $l\in [0,1]$ and x , y , g ∈ E $x,y,g\in \mathbf{E}$ , where E is a real Banach space and K 1 , K 2 : [ 0 , 1 ] × [ 0 , 1 ] × R → R $K_{1},K_{2}:[0,1]\times [0,1]\times \mathbb{R}\to \mathbb{R}$ .

This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, and fixed point results for set-valued fuzzy cone-contraction and for multi-valued fuzzy cone-contraction mappings. We prove a fixed point theorem for multi-valued rational type fuzzy cone-contractions in fuzzy cone metric spaces. Our results extend and improve some results given in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and study the concept of generalized fuzzy cone metric space and to obtain the topology by using G-fuzzy cone metric. Moreover, the existence of common fixed point theorem for contractive map and occasionally weakly compatible map and is investigated in generalized fuzzy cone metric space. [ABSTRACT FROM AUTHOR]

In this paper, we present some weakly compatible and quasi-contraction results for self-mappings in fuzzy cone metric spaces and prove some coincidence point and common fixed point theorems in the said space. Moreover, we use two Urysohn type integral equations to get the existence theorem for common solution to support our results. The two Urysohn type integral equations are as follows: x (l) = ∫ 0 1 K 1 (l , v , x (v)) d v + g (l) , y (l) = ∫ 0 1 K 2 (l , v , y (v)) d v + g (l) , where l ∈ [ 0 , 1 ] and x , y , g ∈ E , where E is a real Banach space and K 1 , K 2 : [ 0 , 1 ] × [ 0 , 1 ] × R → R . [ABSTRACT FROM AUTHOR]

The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, our results enrich and generalize some well-known results in fixed point theory. With the help of new lemmas, our proofs are straight forward. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide an application of integral equations to illustrate the usability of our theory.

Ideas of fuzzy T-Kannan & fuzzy T-Chatterjea type contractive mappings in fuzzy cone metric space are introduced and some fixed point theorems are established for such type of mappings in this paper.

The existence of coincidence point and common fixed point for noncommuting mappings satisfying certain contractive condition in fuzzy cone metric space is established and result is justified by a counter example. By using this result, some common fixed point theorems are also established for generalize contractive conditions. [ABSTRACT FROM AUTHOR]

The main contribution in this paper is to introduce an idea of fuzzy c-distance in fuzzy cone metric space. A common fixed point theorem for contraction mapping is established in fuzzy cone metric space by using fuzzy c-distance. Lastly the theorem is justified by a suitable example. [ABSTRACT FROM AUTHOR]

The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, our results enrich and generalize some well-known results in fixed point theory. With the help of new lemmas, our proofs are straight forward. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide an application of integral equations to illustrate the usability of our theory. [ABSTRACT FROM AUTHOR]