On Coincidence and Fixed-Point Theorems in Symmetric Spaces

Abstract

We give an axiom C.C in symmetric spaces and investigate the relationships between C.C and axioms W3 , W4 , and H.E . We give some results on coinsidence and fixed-point theorems in symmetric spaces, and also, we give some examples for the results of Imdad et al. 2006 .

Absorbing Pairs Facilitating Common Fixed Point Theorems for Lipschitzian Type Mappings in Symmetric Spaces

“…The purpose of this paper is to prove unified theorems in symmetric (semimetric) spaces using the notion of absorbing pairs, which generalize various results due to Soliman et al [20], V. Pant [17], Sastry and Murthy [18], Imdad et al [8], Cho et al [4] and some others.…”

“…Choosing k = 1 in Theorem 2.2, we derive a slightly sharpened form of a theorem due to Cho et al [4] as conditions on the ranges of involved mappings are relatively lightened.…”

“…Proof follows from Theorem 2.2 by setting k = 1. □ Our next theorem is essentially inspired by the Lipschitzian condition utilized in Cho et al [4]. …”

Convergence Axioms on Dislocated Symmetric Spaces

“…Cho et al [8] have introduced 2 : for each ∈ , for each > 0, there corresponds a positive number = ( , ) such that if is a point of such that ( , ) ≥ and is any point of then ( , ) + ( , ) ≥ , 3 : for each positive number there is a positive number = ( ) such that ( , ) + ( , ) ≥ for all in and all , in with ( , ) ≥ . Proof.…”

Common Fixed Points of Generalized Contractive Hybrid Pairs in Symmetric Spaces

“…Abbas and Rhoades 8 obtained common fixed point theorems for hybrid pairs of single-valued and multivalued owc maps defined on a symmetric space see also 9 . For other related fixed point results in symmetric spaces and their applications, we refer to [10][11][12][13][14][15] . The aim of this paper is to obtain fixed point theorems involving hybrid pairs of single-valued and multivalued owc maps satisfying a generalized contractive condition in the frame work of a symmetric space.…”