We find geometric conditions on a four-dimensional almost Hermitian manifold under which the almost complex structure is a harmonic map or a minimal isometric imbedding of the manifold into its twistor space.2010 Mathematics Subject Classification. Primary 53C43, Secondary 58E20, 53C28

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In this article, we present an orthogonal L -contraction mapping concepts and prove a fixed point theorem on orthogonal complete Branciari metric spaces. As an application, we apply our major results to solving integral equations.

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<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>

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