In this paper, we examine the validity of bicomplex versions of some crucial
inequalities with respect to the hyperbolic-valued norm
|
⋅
|
𝕜
{|\cdot|_{\Bbbk}}
and we discuss some topological and geometric
concepts such as completeness, convexity, strict convexity and uniform
convexity in the bicomplex setting with respect to the hyperbolic-valued
norm
∥
⋅
∥
𝔻
,
⋅
{\|\cdot\|_{\mathbb{D},\cdot}}
by defining the concept of
𝔻
{\mathbb{D}}
-normed Banach bicomplex A-module and constructing
𝔻
{\mathbb{D}}
-normed Banach bicomplex
𝔹
ℂ
{\mathbb{BC}}
-modules
l
p
𝕜
(
𝔹
ℂ
)
{l_{p}^{\Bbbk}(\mathbb{BC})}
.
In this paper, we construct the quasi-Banach algebra BC(N) of non-Newtonian
bicomplex numbers and we generalize some topological concepts and
inequalities as Schwarz?s, H?lder?s and Minkowski?s in the set of bicomplex
numbers in the sense of non-Newtonian calculus.
In this paper, we obtain existence of unique common fixed point for a contraction mapping on hyperbolic valued metric spaces, and also develop some coupled coincidence point and common coupled fixed point results for two mappings satisfying various contractive conditions in such spaces. We also give some illustrative examples to validate our results.
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