A Simple Proof of the Polar Decomposition Theorem

In this expository paper, we present a new and easier proof of the Polar Decomposition Theorem. Unlike in classical proofs, we do not use the square root of a positive matrix. The presented proof is accessible to a broad audience.

Fixed Point Results Satisfying Rational Type Contractive Conditions in Complex Valued Metric Spaces – Revisited

In our previous work titled “Fixed Point Results Satisfying Rational type Contractive Conditions in Complex Valued Metric Spaces”[Ann. Math. Sil. 30 (2016), 89-110], some errors has been made in the main results (Theorem 3.1, Theorem 3.7 and Theorem 3.22), that may misguide the readers. This note provides corrections of these errors.

Multipliers of Uniform Topological Algebras

Let E be a complete uniform topological algebra with Arens-Michael normed factors within an algebra isomorphism ϕ. If each factor Eα is complete, then every multiplier of E is continuous and ϕ is a topological algebra isomorphism where M(E) is endowed with its seminorm topology.

Invariant Means on Banach Spaces

In this paper we study some generalization of invariant means on Banach spaces. We give some sufficient condition for the existence of the invariant mean and some examples where we have not it.

On Stability of the Cauchy Functional Equation in Groupoids

We give some stability results for the functional equation a(xy) = a(x) + a(y), where a: G → E, G being a groupoid and E a Banach space.

Some Problems in the Calculus of Variations

We present some results and open problems in the Calculus of Variations.

On Orthogonally Additive Functions With Big Graphs

Let E be a separable real inner product space of dimension at least 2 and V be a metrizable and separable linear topological space. We show that the set of all orthogonally additive functions mapping E into V and having big graphs is dense in the space of all orthogonally additive functions from E into V with the Tychonoff topology.

Lie Derivations on Trivial Extension Algebras

In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be expressed as a sum of a derivation and a center valued map vanishing at commutators. We then apply our results for triangular algebras. Some illuminating examples are also included.

Numerical Solution of Time Fractional Schrödinger Equation by Using Quadratic B-Spline Finite Elements

In this article, quadratic B-spline Galerkin method has been employed to solve the time fractional order Schrödinger equation. Numerical solutions and error norms L2 and L∞ are presented in tables.