On the common fixed points of double sequences of two-parameter nonexpansive semigroups in strictly convex Banach spaces

Authors

  • Rasoul Abazari Department of Mathematics, Ardabil branch, Islamic Azad University, Ardabil, Iran
  • Assadollah Niknam Ferdowsi University of Mashhad and Salman Institute of Higher Education, Mashhad, Iran

DOI:

https://doi.org/10.33044/revuma.2136

Abstract

We obtain some results about common fixed points of strongly continuous two-parameter semigroups of nonexpansive mappings in strictly convex Banach spaces. Also, by using them we characterize common fixed points of double sequences of such semigroups.

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References

R. Abazari and A. Niknam, Existence of ground states for approximately inner two-parameter $C_0$-groups on $C^*$-algebras, Bull. Iranian Math. Soc. 42 (2016), no. 2, 435–446. MR 3498165.

N. Dunford and I. E. Segal, Semi-groups of operators and the Weierstrass theorem, Bull. Amer. Math. Soc. 52 (1946), 911–914. MR 0019218.

E. Hille, On the theory of characters of groups and semi-groups in normed vector rings, Proc. Nat. Acad. Sci. U.S.A. 30 (1944), no. 3, 58–60. MR 0009702.

E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, RI, 1957. MR 0089373.

O. A. Ivanova, Certain theorems on an $n$-parametric semigroup of bounded linear operators and their application in the theory of functions (Russian), Teor. Funkciĭ Funkcional. Anal. i Priložen. Vyp. 2 (1966), 35–41. MR 0199727.

M. Janfada, On two-parameter regularized semigroups and the Cauchy problem, Abstr. Appl. Anal. 2009, Art. ID 415847, 15 pp. MR 2533572.

M. Janfada and A. Niknam, On two-parameter dynamical systems and applications, J. Sci. Islam. Repub. Iran 15 (2004), no. 2, 163–169, 192. MR 2064388.

M. Khanehgir, M. Janfada, and A. Niknam, Inhomogeneous two-parameter abstract Cauchy problem, Bull. Iranian Math. Soc. 31 (2005), no. 2, 71–81, 88. MR 2267072.

A. G. Miamee and H. Salehi, Harmonizability, $V$-boundedness and stationary dilation of stochastic processes, Indiana Univ. Math. J. 27 (1978), no. 1, 37–50. MR 0461657.

A. Niknam, Infinitesimal generators of $C^*$-algebras, Potential Anal. 6 (1997), no. 1, 1–9. MR 1436819.

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983. MR 0710486.

A. Schwarz, Space and time from translation symmetry, J. Math. Phys. 51 (2010), no. 1, 015201, 7 pp. MR 2605834.

T. Suzuki, Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces, Abstr. Appl. Anal. 2006, Art. ID 58684, 10 pp. MR 2211674.

J. A. van Casteren, Generators of Strongly Continuous Semigroups, Research notes in mathematics, 115, Pitman, Boston, 1985.

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Published

2022-12-24

Issue

Vol. 63 No. 2 (2022)

Section

Article

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Copyright (c) 2022 Rasoul Abazari, Assadollah Niknam

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