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Noiri in 1984, Dontchev, Ganster and Reilly in recent years and Reilly and Vamanamurthy in 1983 introduced the notion of perfectly continuous, regular set-connected and clopen functions, respectively. The aim of this paper is to introduce the notion of a new class of functions which is called almost clopen functions including the classes of perfectly continuous, regular set-connected and clopen functions. Furthermore, properties of almost clopen functions are obtained and relationships among almost clopenness, perfect continuity, regular set-connectedness, clopenness and almost continuity are investigated. [ABSTRACT FROM AUTHOR]

By employing a novel idea and simple techniques, we substantially generalize the Turán type inequality for rational functions with real zeros and prescribed poles established by Min [5] to include L pspaces for 1≤ p≤∞while loosing the restriction ρ > 2 at the same time. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate homomorphisms which reserve square-free languages or primitive languages. A characterization of square-free-preserving homomorphisms is presented. We show that every square-free-preserving homomorphism is primitive-preserving. Strongly cube-free-preserving homomorphisms are also studied. [ABSTRACT FROM AUTHOR]

In [2, Theorem 3], Bell and Kappe proved that if d is a derivation of a prime ring R which acts as a homomorphism or an anti-homomorphism on a nonzero right ideal I of R, then d = 0 on R. In the present paper our objective is to extend this result to Lie ideals. The following result is proved: Let R be a 2-torsion free prime ring and U a nonzero Lie ideal of R such that u2 ε U, for all u ε U. If d is a derivation of R which acts as a homomorphism or an anti-homomorphism on U, then either d=0 or U ⫅ Z(R). [ABSTRACT FROM AUTHOR]

This paper gives some characterizations of strongly θ-precontinuous functions. [ABSTRACT FROM AUTHOR]

Let f: ℝ+ → ℝ. The subject is the trace inequality Tr f( A) + Tr f( P2 AP2) ≦ Tr f( P12 AP12) + Tr f( P23 AP23), where A is a positive operator, P1; P2; P3 are orthogonal projections such that P1 + P2 + P3 = I, P12 = P1 + P2 and P23 = P2 + P3. There are several examples of functions f satisfying the inequality (called (SSA)) and the case of equality is described. [ABSTRACT FROM AUTHOR]