Geodesic
Analog of the secant method for Banach spaces
Matematičeskie zametki, Tome 8 (1970) no. 4, pp. 487-492

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An analog of the secant method using successive approximations for an inverse operator is studied. This is a second-order method. The Newton–Kantorovich method of obtaining successive approximations for an inverse operator is a special case of the method discussed here. 
@article{MZM_1970_8_4_a7,
     author = {V. A. Ogneva and V. M. Chern'yshenko},
     title = {Analog of the secant method for {Banach} spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {487--492},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_4_a7/}
}
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V. A. Ogneva; V. M. Chern'yshenko. Analog of the secant method for Banach spaces. Matematičeskie zametki, Tome 8 (1970) no. 4, pp. 487-492. http://geodesic.mathdoc.fr/item/MZM_1970_8_4_a7/