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Hierarchical Minimization Problems and Applications

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Nonlinear Analysis

Part of the book series: Trends in Mathematics ((TM))

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Abstract

In this chapter, several iterative methods for solving fixed point problems, variational inequalities, and zeros of monotone operators are presented. A generalized mixed equilibrium problem is considered. The hierarchical minimization problem over the set of intersection of fixed points of a mapping and the set of solutions of a generalized mixed equilibrium problem is considered. A new unified hybrid steepest descent-like iterative algorithm for finding a common solution of a generalized mixed equilibrium problem and a common fixed point problem of uncountable family of nonexpansive mappings is presented and analyzed.

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Acknowledgments

The work of second author was done during his visit to King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia. He expresses his thanks to KFUPM for providing excellent research facilities.

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Authors and Affiliations

  1. Department of Mathematics, Banaras Hindu University, Varanasi, India

    D. R. Sahu

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, India

    Qamrul Hasan Ansari

  3. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Qamrul Hasan Ansari

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  1. D. R. Sahu
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Correspondence to Qamrul Hasan Ansari .

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Editors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    Qamrul Hasan Ansari

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Sahu, D.R., Ansari, Q.H. (2014). Hierarchical Minimization Problems and Applications. In: Ansari, Q. (eds) Nonlinear Analysis. Trends in Mathematics. Birkhäuser, New Delhi. https://doi.org/10.1007/978-81-322-1883-8_7

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