Abstract
AbstractWe obtain common fixed point results for generalized "Equation missing"-nonexpansive "Equation missing"-subweakly commuting maps on nonstarshaped domain. As applications, we establish noncommutative versions of various best approximation results for this class of maps in certain metrizable topological vector spaces.
Highlights
Introduction and preliminariesLet X be a linear space
A p-norm on X is a real-valued function on X with 0 < p ≤ 1, satisfying the following conditions: (i) x p ≥ 0 and x p = 0 ⇔ x = 0, (ii) αx p = |α|p x p, (iii) x + y p ≤ x p + y p for all x, y ∈ X and all scalars α
It is wellknown that the topology of every Hausdorff locally bounded topological linear space is given by some p-norm, 0 < p ≤ 1
Summary
We extend the concept of R-subweakly commuting maps to nonstarshaped domain in the following way (see [7]): Let f and T be self-maps on the set M having property (N) with q ∈ F( f ). The map T : M → X is said to be completely continuous if {xn} converges weakly to x implies that {Txn} converges strongly to Tx. In 1963, Meinardus [10] employed the Schauder fixed point theorem to prove a result regarding invariant approximation. We establish a general common fixed point theorem for R-subweakly commuting generalized I-nonexpansive maps on nonstarshaped domain in the setting of locally bounded topological vector spaces, locally convex topological vector spaces and metric linear spaces. Our results unify and extend the results of Al-Thagafi [1], Dotson [3], Guseman and Peters [4], Habiniak [5], Hussain and Khan [6], Hussain et al [7], Khan and Khan [9], Sahab et al [13], Shahzad [14,15,16,17,18], and Singh [19]
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