New Fixed Point Theorems for $T_f$ Type Contractive Conditions in 2-Banach Spaces

Abstract

S. Gähler ([14]), 1965, defined the term 2-normed space and A. White ([3]),1968, defined 2-Banach spaces. In paper [12] are proven several theorems about them. The term contractive mapping in 2-normed space was defined by Hatikrishnan and K. T. Ravindran in [8] and R. Kannan ([9]) and S. K. Chatterjea ([15]) theorems are proven by M. Kir and H. Kiziltunc in [4] The further generalizations of these results are elaborated in [1], [6], [10] and [16]. In this paper will be proven several theorems about fixed point for determined types of Tf -contractive mapping in 2-Banach space.2000 Mathematics Subject Classification. Primary: 46J10, 46J15, 47H10.