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Approximation of a common f-fixed point of f-pseudocontractive mappings in Banach spaces

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Abstract

Let E be a real reflexive Banach space with its dual \(E^*\) and f be a proper, convex and lower-semi-continuous function on E. The purpose of this paper is to introduce and study a new class of mappings from E into \(E^*\) called f-pseudocontractive mappings with the notion of f-fixed points. In the case that E is a real  reflexive Banach space and f is a strongly coercive, bounded and uniformly Fréchet differentiable Legendre function which is strongly convex on bounded subsets of E, a sequence is constructed which converges strongly to a common f-fixed point of two f-pseudocontractive mappings. As a consequence, we obtain a scheme which converges strongly to a common zero of monotone mappings. Furthermore, this analog is applied to approximate solutions to convex optimization problems. Our results improve and generalize many of the results in the literature.

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Acknowledgements

The authors express their deep gratitude to the referees and the editor for their valuable comments and suggestions

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Both authors are gratefully acknowledge the funding received from Simons Foundation based at Botswana International University of Science and Technology (BIUST).

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  1. Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Pvt, Palapye, Bag 0016, Botswana

    Habtu Zegeye & Getahun Bekele Wega

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  1. Habtu Zegeye
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Correspondence to Habtu Zegeye.

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Zegeye, H., Wega, G.B. Approximation of a common f-fixed point of f-pseudocontractive mappings in Banach spaces. Rend. Circ. Mat. Palermo, II. Ser 70, 1139–1162 (2021). https://doi.org/10.1007/s12215-020-00549-8

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