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Mixed Variational-like Inequality Problems in Abstract Convex Spaces

Year 2020, Volume: 3 Issue: 2, 59 - 67, 30.06.2020

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.

References

  • [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] 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] 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] C.D. Horvath, Contractibility and generalized convexity, J. Math. Anal. Appl. 156 (1991), 341-357.
  • [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] S. Park, The KKM principle in abstract convex spaces: Equivalent formulations and applications, Nonlinear Anal. 73 (2010), 1028-1042.
  • [7] S. Park, A genesis of general KKM theorems for abstract convex spaces: Revisited, J. Nonlinear Anal. Optim. 4(2) (2013), 127-132.
  • [8] S. Park, Review of recent studies on the KKM theory, II, Nonlinear Funct. Anal. Appl. 19(1) (2014), 143-155.
  • [9] S. Park, A unification of generalized Fan-Browder type alternatives, J. Nonlinear Convex Anal. 17(1) (2016), 1-15.
  • [10] S. Park, Basis of applications of the KKM theory, J. Nat. Acad. Sci., ROK, Nat. Sci. Ser. 55(2) (2016), 1-33.
  • [11] S. Park, A history of the KKM Theory, J. Nat. Acad. Sci., ROK, Nat. Sci. Ser. 56(2) (2017), 1-51.
  • [12] S. Park, The use of weak topologies in the KKM theory, RIMS Kôkyûroku, Kyoto Univ. 2065 (Aug. 31 - Sep. 2, 2016), Apr. 2018, 51-62.
  • [13] S. Park, On further examples of partial KKM spaces, J. Fixed Point Theory, 2019, 2019:10 (18 June, 2019).
  • [14] S. Park, From Hadamard manifolds to Horvath spaces, J. Nat. Acad. Sci., ROK, Nat. Sci. Ser. 58(1) (2019), 1-36.
Year 2020, Volume: 3 Issue: 2, 59 - 67, 30.06.2020

Abstract

References

  • [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] 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] 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] C.D. Horvath, Contractibility and generalized convexity, J. Math. Anal. Appl. 156 (1991), 341-357.
  • [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] S. Park, The KKM principle in abstract convex spaces: Equivalent formulations and applications, Nonlinear Anal. 73 (2010), 1028-1042.
  • [7] S. Park, A genesis of general KKM theorems for abstract convex spaces: Revisited, J. Nonlinear Anal. Optim. 4(2) (2013), 127-132.
  • [8] S. Park, Review of recent studies on the KKM theory, II, Nonlinear Funct. Anal. Appl. 19(1) (2014), 143-155.
  • [9] S. Park, A unification of generalized Fan-Browder type alternatives, J. Nonlinear Convex Anal. 17(1) (2016), 1-15.
  • [10] S. Park, Basis of applications of the KKM theory, J. Nat. Acad. Sci., ROK, Nat. Sci. Ser. 55(2) (2016), 1-33.
  • [11] S. Park, A history of the KKM Theory, J. Nat. Acad. Sci., ROK, Nat. Sci. Ser. 56(2) (2017), 1-51.
  • [12] S. Park, The use of weak topologies in the KKM theory, RIMS Kôkyûroku, Kyoto Univ. 2065 (Aug. 31 - Sep. 2, 2016), Apr. 2018, 51-62.
  • [13] S. Park, On further examples of partial KKM spaces, J. Fixed Point Theory, 2019, 2019:10 (18 June, 2019).
  • [14] S. Park, From Hadamard manifolds to Horvath spaces, J. Nat. Acad. Sci., ROK, Nat. Sci. Ser. 58(1) (2019), 1-36.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Wanbok Lee 0000-0003-1881-8823

Publication Date June 30, 2020
Published in Issue Year 2020 Volume: 3 Issue: 2

Cite

APA Lee, W. (2020). Mixed Variational-like Inequality Problems in Abstract Convex Spaces. Results in Nonlinear Analysis, 3(2), 59-67.
AMA Lee W. Mixed Variational-like Inequality Problems in Abstract Convex Spaces. RNA. June 2020;3(2):59-67.
Chicago Lee, Wanbok. “Mixed Variational-Like Inequality Problems in Abstract Convex Spaces”. Results in Nonlinear Analysis 3, no. 2 (June 2020): 59-67.
EndNote Lee W (June 1, 2020) Mixed Variational-like Inequality Problems in Abstract Convex Spaces. Results in Nonlinear Analysis 3 2 59–67.
IEEE W. Lee, “Mixed Variational-like Inequality Problems in Abstract Convex Spaces”, RNA, vol. 3, no. 2, pp. 59–67, 2020.
ISNAD Lee, Wanbok. “Mixed Variational-Like Inequality Problems in Abstract Convex Spaces”. Results in Nonlinear Analysis 3/2 (June 2020), 59-67.
JAMA 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, 2020, pp. 59-67.
Vancouver Lee W. Mixed Variational-like Inequality Problems in Abstract Convex Spaces. RNA. 2020;3(2):59-67.