Some Operations on Mixed Monotone Operator in Banach Spaces

  • Badrulfalah Badrulfalah Mathematics Department, FMIPA, Universitas Padjajaran, Indonesia
  • I Irianingsih Mathematics Department, FMIPA, Universitas Padjajaran, Indonesia
  • Khafsah Joebaedi Mathematics Department, FMIPA, Universitas Padjajaran, Indonesia
Keywords: nondecreasing and nonincreasing, Mixed monotone operator, Banach space, partial ordering

Abstract

This paper discusses some operations on mixed monotone operator in Banach space, especially addition an multiplication operations. We will prove the sum and product of two mixed monotone operators. The proof using some relevant definitions. The result is the sum o of them is a mixed monotone operator and the product is  too if both  satisfy some conditions

References

[1] Wei L, Agarwal RP. 2018. Simple form of a projection set in hybrid iterative schemes for non-linear mappings, application of inequalities and computational experiments. Journal of inequalities and applications 2018:179
[2] Wei L, Agarwal RP. 2018. New construction and proof techniques of projection algorithm for countable maximal monotone mappings and weakly relatively non-expansive mappings in a Banach space. Journal of inequalities and applications 2018:64
[3] Lochowski RM. 2018. A new inequality for the Riemann-Stieltjes integrals driven by irregular signals in Banach spaces. Journal of inequalities and applications 2018:20
[4] Farid M, Irfan SS, Khan MF, Khan SA. 2017. Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space. Journal of inequalities and applications 2017:297
[5] Wei L, Duan L, Agarwal RP, Chen R, Zheng Y. 2017. Modified forward-backward splitting midpoint method with superposition perturbations for the sum of two kinds of infinite accretive mappings and its applications. Journal of inequalities and applications 2017:227
[6] Sarfaraz M, Ahmad MK, Kilicman A. 2017. Approximation solution for system of generalized ordered variational inclusions with plus sign in circle operator in ordered Banach space. Journal of inequalities and applications 2017:81
[7] Diop C, Sow TM, Djitte N, Chidume CE. 2015. Constructive techniques for zeros of monotone mappings in certain Banach spaces. SpringerPlus 4:383
[8] Li B, Yang D, Yuan W. 2014. Anisotropic hardy spaces of Musielak-Orlicz type with applications to boundedness of sublinear operators. TheScientificWorldJournal 2014:306214
[9] Bartle, Robert. 1992. Introduction to Real Analysis(2nd Edition). John Wiley & Sons. Inc., New York.

[10] Huang, L.G; Zhang, X. 2007. Cone Metric Spaces and Fixed Point Theorems of Contractive Mapping. Journal of Mathematical Analysis And Applications 332, No. 2, pp.1468–1476.
[11] Rosen, K. H. 1994. Discrete Mathematics and Its Applications(3nd Edition). McGraw-Hill, Inc., New York.
[12] Young-Zhou Chen. 1991. Existence of Coupled Fixed Points. Journal of Mathematical Analysis and applications, 154, pp.142-150.
Published
2018-10-30
How to Cite
1.
Badrulfalah B, Irianingsih I, Joebaedi K. Some Operations on Mixed Monotone Operator in Banach Spaces. EKSAKTA [Internet]. 30Oct.2018 [cited 18Jan.2019];19(2):57-1. Available from: http://eksakta.ppj.unp.ac.id/index.php/eksakta/article/view/150

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