Research Article

Mixed Variational-like Inequality Problems in Abstract Convex Spaces

Volume: 3 Number: 2 June 30, 2020
EN

Mixed Variational-like Inequality Problems in Abstract Convex Spaces

Abstract

P.K. Das and G.C. Nayak [3] introduced the concept of generalized variational like inequalities in H-spaces in the presence of $T$-$\eta$-invex function. There the existence theorems of mixed generalized variational like inequalities are studied in H-spaces and also in Riesz spaces in the presence of $T$-$\eta$-invex function. In the present note, we extend their results to partial KKM spaces, which contain H-spaces as very particular subclass.

Keywords

References

  1. [1] C. Bardaro, R. Ceppitelli, Some further generalizations of Knaster-Kuratowski-Mazurkiewicz theorem and minimax in- equalities, J. Math. Anal. Appl. 132(2) (1988), 484-490.
  2. [2] C. Bardaro and R. Ceppitelli, Applications of generalized of Knaster-Kuratowski-Mazurkiewicz theorem to variational inequalities, J. Math. Anal. Appl. 137(1) (1989), 46-58.
  3. [3] P.K. Das and G.C. Nayak, Mixed variational-like inequality problems in H-space, Adv. Nonlinear Variat. Ineq. 22(1) (2019), 14-23.
  4. [4] C.D. Horvath, Contractibility and generalized convexity, J. Math. Anal. Appl. 156 (1991), 341-357.
  5. [5] G.C. Nayak and P.K. Das, S-η-invex function and its associated generalized variational inequalities, PanAmerican Math. J. 24(2) (2014), 41-55.
  6. [6] S. Park, The KKM principle in abstract convex spaces: Equivalent formulations and applications, Nonlinear Anal. 73 (2010), 1028-1042.
  7. [7] S. Park, A genesis of general KKM theorems for abstract convex spaces: Revisited, J. Nonlinear Anal. Optim. 4(2) (2013), 127-132.
  8. [8] S. Park, Review of recent studies on the KKM theory, II, Nonlinear Funct. Anal. Appl. 19(1) (2014), 143-155.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

June 30, 2020

Submission Date

March 18, 2020

Acceptance Date

May 27, 2020

Published in Issue

Year 2020 Volume: 3 Number: 2

APA
Lee, W. (2020). Mixed Variational-like Inequality Problems in Abstract Convex Spaces. Results in Nonlinear Analysis, 3(2), 59-67. https://izlik.org/JA85TB39AA
AMA
1.Lee W. Mixed Variational-like Inequality Problems in Abstract Convex Spaces. RNA. 2020;3(2):59-67. https://izlik.org/JA85TB39AA
Chicago
Lee, Wanbok. 2020. “Mixed Variational-Like Inequality Problems in Abstract Convex Spaces”. Results in Nonlinear Analysis 3 (2): 59-67. https://izlik.org/JA85TB39AA.
EndNote
Lee W (June 1, 2020) Mixed Variational-like Inequality Problems in Abstract Convex Spaces. Results in Nonlinear Analysis 3 2 59–67.
IEEE
[1]W. Lee, “Mixed Variational-like Inequality Problems in Abstract Convex Spaces”, RNA, vol. 3, no. 2, pp. 59–67, June 2020, [Online]. Available: https://izlik.org/JA85TB39AA
ISNAD
Lee, Wanbok. “Mixed Variational-Like Inequality Problems in Abstract Convex Spaces”. Results in Nonlinear Analysis 3/2 (June 1, 2020): 59-67. https://izlik.org/JA85TB39AA.
JAMA
1.Lee W. Mixed Variational-like Inequality Problems in Abstract Convex Spaces. RNA. 2020;3:59–67.
MLA
Lee, Wanbok. “Mixed Variational-Like Inequality Problems in Abstract Convex Spaces”. Results in Nonlinear Analysis, vol. 3, no. 2, June 2020, pp. 59-67, https://izlik.org/JA85TB39AA.
Vancouver
1.Wanbok Lee. Mixed Variational-like Inequality Problems in Abstract Convex Spaces. RNA [Internet]. 2020 Jun. 1;3(2):59-67. Available from: https://izlik.org/JA85TB39AA