Abstract
In this paper we consider, discuss, improve and generalize recent b-(E.A)-property results for mappings in b-metric spaces established by Ozturk and Turkoglu (J Nonlinear Convex Anal 16(10):2059–2066, 2015). Thus, all our results are with much shorter proofs. One example is given to support the result.
Highlights
For a sequenceF and g are satisfy the b-(E.A) property. limn→∞ d fgxn, gfxn exists and it is not equal to 0
Introduction and preliminariesBanach contraction principle (Banach 1922) was proved in 1922
Several interesting results about the existence and uniqueness of fixed point were proved in b-metric spaces (Aghajani et al 2014; AminiHarandi 2014; Bakhtin 1989; Czerwik 1993; Ding et al 2015a, b; Hussain et al 2012, 2013; Jovanović et al 2010; Khamsi and Hussain 2010; Kir and Kiziltunc 2013; Ozturk and Turkoglu 2015; Radenović and Kadelburg 2011; Roshan et al 2013, 2014)
Summary
F and g are satisfy the b-(E.A) property. limn→∞ d fgxn, gfxn exists and it is not equal to 0. Suppose that one of the pairs f , S and g, T satisfy the b-(E.A)-property and that one of the subspaces f (X), g(X), S(X) and T (X) is b-closed in X. Y = max d Tx, Ty , d fx, Tx , d fy, Ty , Suppose that the pair f , T satisfies the b-(E.A)-property and T(X) is closed in X. Suppose that the pair f , T satisfies the b-(E.A)-property and T (X) is closed in X. If the pair f , T is weakly compatible, f and T have a unique common fixed point.
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