• Title/Summary/Keyword: non-Archimedean space

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CHARACTERIZATION ON 2-ISOMETRIES IN NON-ARCHIMEDEAN 2-NORMED SPACES

  • Choy, Jaeyoo;Ku, Se-Hyun
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.1
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    • pp.65-71
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    • 2009
  • Let f be an 2-isometry on a non-Archimedean 2-normed space. In this paper, we prove that the barycenter of triangle is invariant for f up to the translation by f(0), in this case, needless to say, we can imply naturally the Mazur-Ulam theorem in non-Archimedean 2-normed spaces.

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STABILITY OF DRYGAS TYPE FUNCTIONAL EQUATIONS WITH INVOLUTION IN NON-ARCHIMEDEAN BANACH SPACES BY FIXED POINT METHOD

  • KIM, CHANG IL;HAN, GIL JUN
    • Journal of applied mathematics & informatics
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    • v.34 no.5_6
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    • pp.509-517
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    • 2016
  • In this paper, we consider the following functional equation with involution f(x + y) + f(x + σ(y)) = 2f(x) + f(y) + f(σ(y)) and prove the generalized Hyers-Ulam stability for it when the target space is a non-Archimedean Banach space.

ADDITIVE ρ-FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN BANACH SPACE

  • Paokanta, Siriluk;Shim, Eon Hwa
    • The Pure and Applied Mathematics
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    • v.25 no.3
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    • pp.219-227
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    • 2018
  • In this paper, we solve the additive ${\rho}$-functional equations $$(0.1)\;f(x+y)+f(x-y)-2f(x)={\rho}\left(2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)\right)$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < 1, and $$(0.2)\;2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ${\rho}$-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.

THE GENERALIZED HYERS-ULAM STABILITY OF ADDITIVE FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN 2-NORMED SPACE

  • Kim, Chang Il;Park, Se Won
    • Korean Journal of Mathematics
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    • v.22 no.2
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    • pp.339-348
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    • 2014
  • In this paper, we investigate the solution of the following functional inequality $${\parallel}f(x)+f(y)+f(az),\;w{\parallel}{\leq}{\parallel}f(x+y)-f(-az),\;w{\parallel}$$ for some xed non-zero integer a, and prove the generalized Hyers-Ulam stability of it in non-Archimedean 2-normed spaces.

SOME ĆIRIC TYPE FIXED POINT RESULTS IN NON-ARCHIMEDEAN MODULAR METRIC SPACES

  • Hosseini, Hoda;Gordji, Majid Eshaghi
    • The Pure and Applied Mathematics
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    • v.26 no.4
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    • pp.215-231
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    • 2019
  • In this paper, we establish some ĆIRIC type fixed point theorems in α-complete and orbitally T-complete non-Archimedean modular metric spaces. Meanwhile, we present an illustrative example to emphasis the realized improvements. These obtained results extend and improve certain well known results in the literature.

FIXED POINT THEOREMS VIA FAMILY OF MAPS IN WEAK NON-ARCHIMEDEAN MENGER PM-SPACES

  • Singh, Deepak;Ahmed, Amin
    • The Pure and Applied Mathematics
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    • v.20 no.3
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    • pp.181-198
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    • 2013
  • C. Vetro [4] gave the concept of weak non-Archimedean in fuzzy metric space. Using the same concept for Menger PM spaces, Mishra et al. [22] proved the common fixed point theorem for six maps, Also they introduced semi-compatibility. In this paper, we generalized the theorem [22] for family of maps and proved the common fixed point theorems using the pair of semi-compatible and reciprocally continuous maps for one pair and R-weakly commuting maps for another pair in Menger WNAPM-spaces. Our results extends and generalizes several known results in metric spaces, probabilistic metric spaces and the similar spaces.

Hyers-Ulam Stability of Cubic Mappings in Non-Archimedean Normed Spaces

  • Mirmostafaee, Alireza Kamel
    • Kyungpook Mathematical Journal
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    • v.50 no.2
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    • pp.315-327
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    • 2010
  • We give a xed point approach to the generalized Hyers-Ulam stability of the cubic equation f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 12f(x) in non-Archimedean normed spaces. We will give an example to show that some known results in the stability of cubic functional equations in real normed spaces fail in non-Archimedean normed spaces. Finally, some applications of our results in non-Archimedean normed spaces over p-adic numbers will be exhibited.

A NOTE ON DISCRETE SEMIGROUPS OF BOUNDED LINEAR OPERATORS ON NON-ARCHIMEDEAN BANACH SPACES

  • Blali, Aziz;Amrani, Abdelkhalek El;Ettayb, Jawad
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.409-414
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    • 2022
  • Let A ∈ B(X) be a spectral operator on a non-archimedean Banach space over an algebraically closed field. In this note, we give a necessary and sufficient condition on the resolvent of A so that the discrete semigroup consisting of powers of A is uniformly-bounded.

GENERALIZED HYERS-ULAM STABILITY OF CUBIC TYPE FUNCTIONAL EQUATIONS IN NORMED SPACES

  • KIM, GWANG HUI;SHIN, HWAN-YONG
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.3
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    • pp.397-408
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    • 2015
  • In this paper, we solve the Hyers-Ulam stability problem for the following cubic type functional equation $$f(rx+sy)+f(rx-sy)=rs^2f(x+y)+rs^2f(x-y)+2r(r^2-s^2)f(x)$$in quasi-Banach space and non-Archimedean space, where $r={\neq}{\pm}1,0$ and s are real numbers.