Coupled fixed point theorems on $ \mathcal{C}^\star $-algebra valued bipolar metric spaces

Abstract

<abstract><p>In the present paper, we introduce the notion of a $ \mathcal{C}^{\star} $-algebra valued bipolar metric space and prove coupled fixed point theorems. Some of the well-known outcomes in the literature are generalized and expanded by the results shown. An example and application to support our result is presented.</p></abstract>

Fixed Points on Covariant and Contravariant Maps with an Application

“…For further details on C -algebra, please refer to [28][29][30][31]. Recently, Guna et al [25] introduced the notion of C -algebra-valued bipolar metric space and proved fixed-point results therein. Inspired by the proven results, we establish fixed-point results in the setting of C -algebra-valued bipolar metric space and find its application to prove the existence of unique solutions to integral equations.…”

Solving a Fractional Differential Equation via the Bipolar Parametric Metric Space

“…In 2021, Gaba et al [10] proved FP theorems on BPMS. Mani et al [11] developed the concept and proved coupled fxed point theorems in C ⋆ algebravalued bipolar metric spaces (see [12][13][14]).…”

Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in C*-Algebra Valued Bipolar b-Metric Spaces

“…Recently in 2022, Mani et al [16] presented the concept of C * -algebra valued bipolar metric space as a generalization of C * -algebra valued (introduced by Ma et al, in 2014) [9] and bipolar metric space (introduced by Mutlu and Gürdal in 2016) [12] and established fixed point theorems on C * -algebra valued bipolar metric space.…”

“…In 2022, Mani et al [16] gave the following: 16]). Consider a unital C * -algebra A with a unital I A , two sets Σ, Π = φ, and…”