SOME NEW FIXED POINT THEOREMS IN 2-BANACH SPACES

Abstract

S. Gähler ([9]), 1965, defined the 2-normed space, A. White ([3]), 1968, defined the 2-Banach space. Several statements about them are proven in [7]. P. K. Hatikrishnan and K. T. Ravindran in [5] defined the contractive mapping in 2-normed space. M. Kir and H. Kiziltunc in [3] by applying the above theorem, proved the generalizations of R. Kannan ([6]) and S. K. Chatterjea ([10]) theorem. Further generalizations of these results are elaborated in [1] and [11]. In this paper we will generalize the above results by using the class \(\Theta\) of monotony increasing functions \(f:[0,+\infty)\to\mathbb{R}\) such that \(f^{-1}(0)=\{0\}\) holds true.