An Ulam stability result on quasi-b-metric-like spaces

Abstract

Abstract:In this paper a class of general type˛-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.

Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations

“…This means that under the above conditions, the integro-differential equation (1) has the semi-Hyers-Ulam-Rassias stability.…”

“…where θ ≥ 0, there is a solution y 0 of the integro-differential equation (1) and a constant C > 0 independent of y and y 0 such that…”

“…for some non-negative function σ defined on [a, b], then we say that the integro-differential equation (1) has the semi-Hyers-Ulam-Rassias stability.…”

A Proposal for Revisiting Banach and Caristi Type Theorems in b-Metric Spaces

“…On the other hand, this concept became popular after the interesting papers of Bakhtin [3] and Czerwik [4]. For more details in b-metric space and advances in fixed point theory in the setting of b-metric spaces, we refer e.g., [5][6][7][8][9][10][11][12][13][14][15][16][17]. Definition 1.…”

Some Results on (s − q)-Graphic Contraction Mappings in b-Metric-Like Spaces

“…It is clear that each metric-like space, i.e., each partial b-metric space, is a b-metric-like space, while the converse is not true. For more such examples and details see [1,2,[5][6][7][15][16][17][18][19][20][21][22][23][24][25][26][27]. Moreover, for various metrics in the context of the complex domain see [28,29].…”