The purpose of this paper is to introduce (λ, ρ)-quasi firmly nonexpansive mappings in context of modular function spaces and to prove some basic properties and approximation results for fixed point for these mappings. Further we discuss the concept of summably almost T-stability and also some examples are provided to support our results.
The (W.C.C) condition was developed by K.P.R. Rao et al. in 2013 which established common fixed point results in partial metric spaces. By using Hausdorff metric-like space, we obtain Suzuki type common fixed point theorems for hybrid pair of maps in metric-like spaces. We observe different conditions about maps to obtain a fixed point. In addition, as consequence of our main result, we study the existence of a common solution for a class of functional equations originating in dynamic programming.
This research article introduces a new iterative process called MP iteration and proves some convergence and approximation results for the xed points of ρ-nonexpansive mappings in modular function spaces. To demonstrate that MP iterative process converges faster than some well-known existing iterative processes for ρ-nonexpansive mappings, we construct some numerical examples. In the end, the concept of summably almost T-stability for MP iterative process is discussed.
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