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      General solution and Ulam-Hyers stability of viginti functional equations in multi-Banach spaces

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      https://www.riss.kr/link?id=A105350383

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      다국어 초록 (Multilingual Abstract)

      In this paper, we introduce the general form of a viginti functional equation. Then, we find the general solution and study the generalized Ulam-Hyers stability of such functional equation in multi-Banach spaces by using fixed point technique. Also, w...

      In this paper, we introduce the general form of a viginti functional equation. Then, we find the general solution and study the generalized Ulam-Hyers stability of such functional equation in multi-Banach spaces by using fixed point technique. Also, we indicate an example for non-stability case regarding to this new functional equation.

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      참고문헌 (Reference)

      1 J. M. Rassias, "Various generalized Ulam-Hyers Stabilities of a nonic functional equations" 9 : 159-196, 2016

      2 K. Ravi, "Ulam-Hyers stability of undecic functional equation in quasi-beta normed spaces fixed point method" 9 : 83-103, 2016

      3 A. Bodaghi, "Ulam's type stability of a functional equation deriving from quadratic and additive functions" 9 : 73-84, 2015

      4 A. Bodaghi, "The mixed cubic-quartic functional equation" LXIII : 215-227, 2017

      5 A. Bodaghi, "The generalized cubic functional equation and the stability of cubic Jordan ∗-derivations" 59 : 235-250, 2013

      6 K. W. Jun, "The generalized Hyers-Ulam-Russias stability of a cubic functional equation" 274 : 867-878, 2002

      7 Mohan Arunkumar, "THE GENERAL SOLUTION AND APPROXIMATIONS OF A DECIC TYPE FUNCTIONAL EQUATION IN VARIOUS NORMED SPACES" 충청수학회 29 (29): 287-328, 2016

      8 A. Bodaghi, "Stability of the general form of quadratic-quartic functional equations in non-Archimedean L-fuzzy normed spaces" 11 (11): 15-29, 2018

      9 H. G. Dales, "Stability of mappings on multi-normed spaces" 49 : 321-332, 2007

      10 A. Bodaghi, "Stability of a quartic functional equation" 2014

      1 J. M. Rassias, "Various generalized Ulam-Hyers Stabilities of a nonic functional equations" 9 : 159-196, 2016

      2 K. Ravi, "Ulam-Hyers stability of undecic functional equation in quasi-beta normed spaces fixed point method" 9 : 83-103, 2016

      3 A. Bodaghi, "Ulam's type stability of a functional equation deriving from quadratic and additive functions" 9 : 73-84, 2015

      4 A. Bodaghi, "The mixed cubic-quartic functional equation" LXIII : 215-227, 2017

      5 A. Bodaghi, "The generalized cubic functional equation and the stability of cubic Jordan ∗-derivations" 59 : 235-250, 2013

      6 K. W. Jun, "The generalized Hyers-Ulam-Russias stability of a cubic functional equation" 274 : 867-878, 2002

      7 Mohan Arunkumar, "THE GENERAL SOLUTION AND APPROXIMATIONS OF A DECIC TYPE FUNCTIONAL EQUATION IN VARIOUS NORMED SPACES" 충청수학회 29 (29): 287-328, 2016

      8 A. Bodaghi, "Stability of the general form of quadratic-quartic functional equations in non-Archimedean L-fuzzy normed spaces" 11 (11): 15-29, 2018

      9 H. G. Dales, "Stability of mappings on multi-normed spaces" 49 : 321-332, 2007

      10 A. Bodaghi, "Stability of a quartic functional equation" 2014

      11 A. Bodaghi, "Stability of a mixed type additive and quartic function equation" 28 (28): 1629-1640, 2014

      12 J. M. Rassias, "Solution of the Ulam stability problem for quartic mappings" 34 : 243-252, 1999

      13 J. M. Rassias, "Solution of the Ulam stability problem for cubic mappings" 36 (36): 63-72, 2001

      14 P. Narasimman, "Solution and stability of a mixed type functional equation" 31 : 1229-1239, 2017

      15 M. Turinici, "Sequentially iterative processes and applications to Volterra func- tional equations" 32 : 127-134, 1978

      16 Madjid Eshaghi Gordji, "STABILITY OF A FUNCTIONAL EQUATION DERIVING FROM QUARTIC AND ADDITIVE FUNCTIONS" 대한수학회 47 (47): 491-502, 2010

      17 F. Skof, "Propriet localie approssimazione di operatori" 53 : 113-129, 1983

      18 S. Czerwik, "On the stability of the quadratic mapping in normed spaces" 62 : 59-64, 1992

      19 T. Aoki, "On the stability of the linear transformation in Banach spaces" 2 : 64-66, 1950

      20 M. Rassias, "On the stability of the linear mapping in Banach spaces" 72 : 297-300, 1978

      21 D. H. Hyers, "On the stability of the linear functional equation" 27 : 222-224, 1941

      22 D. Mihet, "On the stability of the additive Cauchy functional equation in random normed spaces" 343 : 567-572, 2008

      23 Z. Gajda, "On stability of additive mappings" 14 : 431-434, 1991

      24 A. Bodaghi, "Intuitionistic fuzzy stability of the generalized forms of cubic and quartic functional equations" 30 : 2309-2317, 2016

      25 K. Ravi, "General solution and stability of quattuordecic functional equation in quasi beta-normed spaces" 6 : 921-941, 2016

      26 Abasalt Bodaghi, "Fundamental stabilities of the nonic functional equation in intuitionistic fuzzy normed spaces" 대한수학회 31 (31): 729-743, 2016

      27 J. M. Rassias, "Fixed points and stability of nonic functional equation in quasi-${\beta}$-normed spaces" 3 : 293-309, 2015

      28 T. Z. Xu, "Approximate septic and octic mappings in quasi-${\beta}$- normed spaces" 15 (15): 1110-1119, 2013

      29 A. Bodaghi, "Approximate mixed type additive and quartic functional equation" 35 : 43-56, 2017

      30 J. B. Diaz, "A fixed point theorem of the alternative for contractions on a generalized complete metric space" 74 : 305-309, 1968

      31 T. Z. Xu, "A fixed point approach to the stability of quintic and sextic functional equations in quasi-${\beta}$-normed spaces" 2010

      32 T. Z. Xu, "A generalized mixed quadratic-quartic functional equation" 35 : 633-649, 2012

      33 P. Gavruta, "A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings" 184 : 431-436, 1994

      34 S. M. Ulam, "A Collection of the Mathematical Problems" Interscience 1960

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