In this paper, we propose and study a multi-step iterative algorithm that comprises of a finite family of asymptotically $ k_i $-strictly pseudocontractive mappings with respect to $ p, $ and a $ p $-resolvent operator associated with a proper convex and lower semicontinuous function in a $ p $-uniformly convex metric space. Also, we establish the $ \Delta $-convergence of the proposed algorithm to a common fixed point of finite family of asymptotically $ k_i $-strictly pseudocontractive mappings which is also a minimizer of a proper convex and lower semicontinuous function. Furthermore, nontrivial numerical examples of our algorithm are given to show its applicability. Our results complement a host of recent results in literature.
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Errors vs Iteration numbers(n) for Example 4.1: Case 1 (top left); Case 2 (top right); Case 3 (bottom left); Case 4 (bottom right)
Errors vs Iteration numbers(n) for Example 4.2: Case 1 (top left); Case 2 (top right); Case 3 (bottom left); Case 4 (bottom right)