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We introduce the concept of stability of a k-step fixed point iterative method xn+1=T(xn,xn−1,…,xn−k+1)Open image in new window, n≥k−1Open image in new window, and study the stability of this equation for mappings T:Xk→XOpen image in new window satisfying some Prešić type contraction conditions. Our results naturally extend various stability results of fixed point iterative methods in literature, from contractive self-mappings T:X→XOpen image in new window to Prešić type contractive mappings T:Xk→XOpen image in new window. Illustrative examples of both stable and unstable fixed point iterations are also presented.

Stability of k-step fixed point iterative methods for some Prešić type contractive mappings