Fixed Point Theorems for Multivalued Mappings in Symmetric Spaces

Abstract

Abstract. In this paper we prove some fixed point theorems for multivalued mappings using rational inequality in a symmetric space. These results are generalizations of some well known results in metric spaces and also in the setting of symmetric spaces.

Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space

“…Over the years, it has been known that many researchers have written about fixed-point theorems for multivalued left and right contractions in the sense of Nadler, such as Rus (2008) [28]; Nadler (1969) [5]; Mureşan (2002) [24]; Bucur (2019) [14]; Bucur, Guran, and Petruşel (2009) [15]; and Joshi, L.K. and Dimri (2007) [23]. In this paper, we defined two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space, and demonstrated some fixed point theorems for them.…”

“…; Joshi, L.K. ; and Dimri [23] studied the existence of fixed points in symmetric spaces, demonstrating that for these theorems it is not necessary to apply all the axioms from the definition of a metric.…”