2–Cone Banach spaces and fixed point theorem

Abstract

A theorem proving the irreversibility of the biological arrow of time, based on fixed points in the brain as a compact, Δ-complete topological space AIP Conf.Abstract. The present article deals with 2−cone normed spaces, 2−cone Banach spaces. Also, some results expressing under what conditions a self-mapping T of 2−cone Banach space (X, ., . c ) has a unique fixed point are given.

Common Fixed Point Theorems Satisfying Implicit Relations on 2-cone Banach Space with an Application

“…Definition 1.7. [16] Let X be a linear space over R with dimension greater then or equal to 2, E be Banach space with the norm . and P ⊂ E be a cone.…”

“…In [4], Karapınar established some fixed-point theorems in cone Banach space in 2009. AhmetŞahiner and Tuba Yigit initiated the concept of a 2-cone Banach space and proved some fixed-point theorems [16]. Krishnakumar and Dhamodharan proved some common fixed-point theorems on contractive modulus in 2-cone Banach space [5].…”

Existence of Fixed Point Theorems in a Linear 2-Normed Spaces

“…Here after, many authors establish the fixed point theorem in 2-normed spaces and 2-Banach spaces, See [4,6,[16][17][18][19][20]. Recently, generalise the concept of 2-normed space as well as 2-Banach space into 2-cone Banach space [3,12,22]. We now state some definitions before presenting our main results.…”

Common fixed point of contractive modulus on 2-cone Banach space

“…The common fixed point theorems with the assumption of weakly compatible and coincidence point of four maps on an upper semi continuous contractive modulus in cone Banach space are proved by R. Krishnakumar and D.Dhamodharan [5]. Ahmet Sahiner and Tuba Yigit [11] proved 2 -cone Banach spaces and fixed point theorem.…”