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Mathematical Analysis and its Applications pp 159–168Cite as

Applications of Generalized Monotonicity to Variational-Like Inequalities and Equilibrium Problems

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 143))

Abstract

In this paper, we introduce the concept of relaxed (\(\rho \)-\(\theta \))-\(\eta \)-invariant monotonicity to establish the existence of solutions for variational-like inequality problems in reflexive Banach spaces. Again we introduce the concept of (\(\rho \)-\(\theta \))-monotonicity for bifunctions. The existence of solution for equilibrium problem with (\(\rho \)-\(\theta \))-monotonicity is established by using the KKM technique.

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Authors and Affiliations

  1. Indian Institute of Information Technology, Design and Manufacturing Jabalpur, 482 005, Jabalpur, India

    N. K. Mahato

  2. University of Central Florida, Orlando, 32816, FL, USA

    R. N. Mohapatra

Authors
  1. N. K. Mahato
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  2. R. N. Mohapatra
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Corresponding author

Correspondence to R. N. Mohapatra .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    P. N. Agrawal

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    R. N. Mohapatra

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Uaday Singh

  4. Dept. of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

    H. M. Srivastava

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Mahato, N.K., Mohapatra, R.N. (2015). Applications of Generalized Monotonicity to Variational-Like Inequalities and Equilibrium Problems. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_12

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