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COMONOTONE APPROXIMATION IN LINEAR 2-NORMED SPACES
MEHMET AÇIKGÖZ 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.2
In this paper, we extend the notion of comonotone approximation to linear 2-normed spaces. We shall study comonotone approximation of finite dimensional linear 2-normed spaces in the sense of simultaneous and best si-multaneous approximation. We give and prove some results and theorems on characterization and uniqueness of comonotone approximation. In this spaces,our results coincide with the usual one.
A STUDY ON TYPES OF APPROXIMATION IN THE SENSE OF 2-STRUCTURES
MEHMET AÇIKGÖZ,YUSUF KARAKUS,DOGAN DÖNMEZ 장전수학회 2011 Proceedings of the Jangjeon mathematical society Vol.14 No.1
The problem of approximation and best approximation has been studied by many mathematicians. Most of works have dealt with the existence,uniqueness and characterization of approximation and best approximations in spaces of continuous functions with values in Banach spaces. But little or no work on approximation has been done in the sense of 2-structures such 2-normed sapaces, generalized 2-normed spaces and 2-Banach spaces. The aim of this paper is to give the types of approximation and investigate the approx-imation in the sense of these spaces. In addition, we shall give some results and related examples on the sets of approximation and coapproximation.
A unified generating function of the q-genocchi polynomials with their interpolation functions
Serkan Araci,MEHMET AÇIKGÖZ,HASSAN JOLANY,서종진 장전수학회 2012 Proceedings of the Jangjeon mathematical society Vol.15 No.2
The purpose of this paper is to construct of the uni cation q-extension Genocchi polynomials. We give some interesting relations of this type of polynomials. Finally, we derive the q-extensions of Hurwitz-zeta type functions from the Mellin transformation of this generating function which interpolates the uni ed of q-extension of Genocchi polynomials.