‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

Let M be a metric space with a finite diameter D and a finite normalized measure μM. Let the Hilbert space L2(M) of complex-valued functions be decomposed into a countable (whenM is infinite) or finite (with D+ 1 members whenM is finite) direct sum of mutually orthogonal subspaces L2(M) = V0 ⊕ V1 ⊕ · · · (V0 is the space of constant functions). We denote N = D + 1 ifM is finite and N = ∞ otherw...

Gauge theories commonly employ complex vector-valued fields to reduce symmetry groups through the Higgs mechanism of spontaneous symmetry breaking. The geometry of the internal space V is tacitly assumed to be the metric geometry of some static, nondynamical hermitian metric k. In this paper, we consider G-principal bundle gauge theories, where G is a subgroup of U(V ,k) (the unitary transforma...

The purpose of this paper is to study common fixed point theorems for six (four single-valued and two set-valued) mappings in fuzzy metric space using general contractive condition of integral type, without assuming compatibility and continuity of any mapping on non complete metric spaces. To prove the theorems, we use a non compatible condition, that is, weak commutativity of type (Kh)in fuzzy...

In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...

‎Recently‎, ‎Hussain et al.‎, ‎discussed the concept of $wt$-distance on a‎ ‎metric type space‎. ‎In this paper‎, ‎we prove some fixed‎ ‎point theorems for classes of contractive type multi-valued operators‎, ‎by using $wt$-distances in the setting of a complete metric type space‎. ‎These results generalize a result of Feng and Liu on multi-valued operators.

Metric fixed point theory has vast applications in various domain areas, as it helps finding analytical solutions under contractive conditions, including non-linear integral-type contractions. In our present work, we have established results the setting of complex valued partial metric space. Our extend proven literature. Using main result, provided an application to find solution Urysohn-type ...