Some surjectivity theorems with applications

Some Surjectivity Theorems with Applications

In this paper a new class of mappings, known as locally λ-strongly φ-accretive mappings, where λ and φ have special meanings, is introduced. This class of mappings constitutes a generalization of the well-known monotone mappings, accretive mappings and strongly φ-accretive mappings. Subsequently, the above notion is used to extend the results of Park and Park, Browder and Ray to locally λ-stron...

Some Liouville theorems and applications

We give exposition of a Liouville theorem established in [6] which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof of the classical Liouville theorem for harmonic functions. Applications of the Liouville theorem, as well as that of earlier ones in [5], can be found in [6, 7] an...

Some Theorems and Applications of Ramsey Theory

We present here certain theorems in Ramsey theory and some of their applications. First is Ramsey’s Theorem, which concerns the existence of monochromatic complete subgraphs of colored graphs that are large enough. One application is Schur’s Theorem, which is used for a result relating to Fermat’s Last Theorem. We then present the Hales-Jewett Theorem, which can be used to prove van der Waerden...

Some Applications of Fixed Point Theorems

Some Theorems and Applications of the (q, r)-Whitney Numbers

The (q, r)-Whitney numbers were recently defined in terms of the q-Boson operators, and several combinatorial properties which appear to be q-analogues of similar properties were studied. In this paper, we obtain elementary and complete symmetric polynomial forms for the (q, r)-Whitney numbers, and give combinatorial interpretations in the context of A-tableaux. We also obtain convolution-type ...