Ulam-Hyers Stability Results for Fixed Point Problems via --Contractive Mapping in ()-Metric Space

Abstract

We will investigate some existence, uniqueness, and Ulam-Hyers stability results for fixed point problems via --contractive mapping of type-() in the framework of -metric spaces. The presented theorems extend, generalize, and unify several results in the literature, involving the results of Samet et al. (2012).

On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory

“…Consequently, the notion of -metric is more general than the standard metric. For the sake of completeness, we recollect standard but interesting three examples of -metric spaces; see, for example, [6,7] and the related references therein.…”

Fuzzy fixed point theorems for multivalued fuzzy contractions in b -metric spaces

“…Since then, a number of authors investigated fixed point theorems for single-valued and miltivalued mappings in b-metric spaces (see [3,4,7,8,9,10,11,12,14,16,17,22,31] and references therein).…”

A New Class of Contraction inb-Metric Spaces and Applications

“…In this interesting paper, Czerwik [1] generalized the Banach contraction principle in the context of complete b-metric spaces. After that many researchers reported the existence and uniqueness of fixed points of various operators in the setting of b-metric spaces (see, e.g., [2][3][4][5][6][7][8][9][10][11][12][13] and some references therein).…”