A NOVEL DOUBLE-APPLICATION HA-ITERATION FORGENERALIZED (α,β)-NONEXPANSIVE MAPPINGS: FIXED POINTSTRUCTURE AND CONVERGENCE THEORY
Keywords:
Generalized (α,β) non-expansive mapping, HA-iteration , Banach space, rate of convergenceAbstract
We study generalized (α,β)-nonexpansive (G(α,β)NE) mappings in Banach spaces and approximate their fixed points through the HA-iteration, a three-step scheme built on a double application of the underlying operator Q at each stage. This double application is the key structural feature driving the theory: it yields sharpened bound edness and ∆-type characterizations of the fixed point set, a demiclosed principle, and strong and weak convergence theorems for the HA-iteration in uniformly convex Banach spaces. The results extend and unify several related results on fixed point approximation for generalized nonexpansive-type mappings.
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Copyright (c) 2026 Saima Bhatti, Fatima Abbas, Hanif Ullah, Khalida Mir Alam, Soumyarani Mishra (Author)
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