Random variational-like inclusion and random proximal operator equation for random fuzzy mappings in Banach spaces

In this paper, we introduce and study a random variational-like inclusion and its corresponding random proximal operator equation for random fuzzy mappings. It is established that the random variational-like inclusion problem for random fuzzy mappings is equivalent to a random fixed point problem. We also establish a relationship between random variational-like inclusion and random proximal operator equation for random fuzzy mappings. This equivalence is used to define an iterative algorithm for solving random proximal operator equation for random fuzzy mappings. Through an example, we show that the random Wardrop equilibrium problem is a special case of the random variational-like inclusion problem for random fuzzy mappings

Coupled Fixed Point Theorems in Partially Ordered Metric Space

Abstract: - There is several generalization of Banach contraction principle. Recently Bhaskaran and Lakshmikantham generalized this result and prove coupled fixed point theorems in ordered metric space. In this present work, we proof some coupled fixed point theorems in ordered metric space. Key words: - Ordered Metric Space, Fixed point, Coupled Fixed point, mixed monotone property

F-closed sets and coupled fixed point theorems without the mixed monotone property

In this paper we present the notion of F-closed set (which is weaker than the concept of F-invariant set introduced in Samet and Vetro (Ann. Funct. Anal. 1:46-56, 2010), and we prove some coupled fixed point theorems without the condition of mixed monotone property. Furthermore, we interpret the transitive property as a partial preorder and, then, some results in that paper and in Sintunavarat et al. (Fixed Point Theory Appl. 2012:170, 2012) can be reduced to the unidimensional case

Ulam stability of hom-ders in fuzzy Banach algebras

This paper aims to investigate a new type of derivations in a fuzzy Banach algebra. Moreover, by using the fixed point method, we obtain some stability results of the hom-der in fuzzy Banach algebras associated with the functional equation $f(x+{\textbf{k}}y) = f(x)+{\textbf{k}}f(y)$ where ${\textbf{k}}$ is a fixed positive integer greater than $1$

Set-Valued Analysis

This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers

Common new fixed point results on b-cone Banach spaces over Banach algebras

[EN] Recently Zhu and Zhai studied the concepts of cone b-norm and cone b-Banach space as generalizations of cone b-metric spaces and theygave a definition of φ-operator and obtained some new fixed point theorems in cone b-Banach spaces over Banach algebras by using φ-operator. In this paper we propose a notion of quasi-cone over Banach algebras, then by utilizing some new conditions and following their work with introducing two mappings T and S we improve the fixed point theorems to the commonfixed point theorems. An example is given to illustrate the usability of the obtained results.Afshari, H.; Shojaat, H.; Fulga, A. (2022). Common new fixed point results on b-cone Banach spaces over Banach algebras. Applied General Topology. 23(1):145-156. https://doi.org/10.4995/agt.2022.15571OJS14515623