Abstract We utilize Hardy-Rogers contraction and CJM−contraction in a C * −algebra valued partial metric space to create an environment establish fixed point. Next, we present examples elaborate on the novel validate our result. conclude paper by solving boundary value problem matrix equation as applications of main results which demonstrate significance motivation for such investigations.

Let D be the open unit disk in the complex plane and ∂D the unit circle. Let dσ(w) be the normalized Lebesgue measure on the unit circle. We denote by L(C) (L for n=1) the space of C-valued Lebesgue square integrable functions on the unit circle. The Hardy space H(C) (H for n=1) is the closed linear span of C-valued analytic polynomials. We observe that L(C) = L ⊗ C and H(C) = H ⊗ C, where ⊗ de...

Free interpolation in Hardy spaces is characterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces H, p > 0. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class)...

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...