Some topological properties and fixed point results in cone metric spaces over Banach algebras

Dislocated quasi cone b-metric space over Banach algebra and contraction principles with application to functional equations

“…The concept of cone b-metric space (in short CbMS) over a Banach algebra was introduced in [1] and the authors proved generalised contraction principles in this space which directly improved and extended many comparable results in b-metric spaces (See [2][3][4]). α-admissible mappings were introduced by Samet et al [5] which further helped in weakening and generalizing many contractive conditions (See [6][7][8]).…”

On Generalized Hardy–Rogers Type α-Admissible Mappings in Cone b-Metric Spaces over Banach Algebras

“…We begin with the definitions of known notions as well as known results from cone metric and cone b-metric spaces (for more details see [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]) over Banach algebra, respectively. Definition 1.…”

Fixed Point Results under Generalized c-Distance in Cone b-Metric Spaces Over Banach Algebras

“…The results of Liu and Xu are significant, in the sense that cone metric spaces over a Banach algebra are not equivalent to metric spaces. Hence, some interesting results about fixed point theory in cone metric spaces over a Banach algebra and in cone b-metric spaces over a Banach algebra with its applications were proved in [4][5][6].…”

“…Obviously, for s = 1, a cone b-metric space over a Banach algebra A is a cone metric space over same Banach algebra A. In addition, for definitions such as convergent and Cauchy sequences, c-sequence, completeness, continuity, and examples in cone b-metric spaces over Banach algebra A, we refer to [5,6]. In the sequel, let P be a solid cone and (X, d) be a cone b-metric space over a Banach algebra A with coefficient s ≥ 1.…”