Some new fixed point theorems in 2-normed spaces

Abstract

In this paper, we introduce and prove some new fixed point theorems in 2-normed spaces.

Extending Kannan and Chatterjea Theorems in 2-Banach Spaces by Using Sequentially Convergent Mapping

“…Hatikrishnan and Ravindran in [4], proved that a contractive mapping has a unique fixed point in a closed and bounded subset of 2-Banach space. Furthermore, M. Kir and H. Kiziltunc in [2] proved that if L is 2-Banach space and for 1 then, S has a unique fixed point in L . The case where the condition (1) is satisfied is actually a generalization of Kannan's Theorem and the case where the condition (2) is satisfied is a generalization of Chatterjea's Theorem.…”

“… , the arithmetic-geometric inequality mean and the theorem 1, directly imply the statement.. ■ 32 A. Malčeski, A. Ibrahimi, R. Malčeski The inequality sated in the condition implies (3), and the required statement is directly implied by the theorem 1. ■  , imply the validity of the theorem 1 and the consequences 1 and 2,[10], and the consequence 3, imply the validity of the theorem 1,[2]. The inequality given in the condition implies the inequality(5).…”

Sequentially Convergent Mappings and Common Fixed Points of Mappings in 2-Banach Spaces

“…Regarding contraction mapping Hatikrishnan and Ravindran in [6] proved that contraction mapping has a unique fixed point in closed and restricted subset of 2-Banach space. Further, in [1], [4], [5] and [7] are proven more results related to fixed points of contraction mapping of 2-Banach spaces, and in [7] are proven several results for common fixed points of contraction mapping defined on the same 2-Banach space.…”

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

“…P. K. Hatikrishnan and K. T. Ravindran in [8] proved that contractive mapping has a unique fixed point in closed and bounded subset in 2-Banach space. In [4] M. Kir and H. Kiziltunc in 2-normed space made generalizations for the theorems about fixed point of R. Kannan ([9]) and S. K. Chatterjea ([15]). For 2-Banach spaces in [1], [6], [10] and [16], by application of Sequentialy Convergent Mappings, several generalizations for already known theorems about fixed point and sharing fixed point are given.…”