# Geometrical Elucidations and Approximation of some Functional Equations in Numerous Variables

Keywords:
Reciprocal-quadratic function, generalized Ulam-Hyers stability, quasi-beta-normed space.

### Abstract

The objective of this paper is to introduce a reciprocal-quadratic difference functional equation and a reciprocal-quadratic adjoint functional equation in copious variables with their geometrical interpretations in Physics and to determine their fundamental stabilities connected with Ulam stability theory in quasi-beta-normed spaces.

### References

Aoki T (1950) On the stability of the linear transformation in

Banach spaces J Math Soc Japan 2 64-66

Bodaghi A and Ebrahimdoost Y (2016) On the stability of

quadratic reciprocal functional equation in nonArchimedean fields Asian-Euro J Math 9 1-9

Gavruta P (1994) A generalization of the Hyers-Ulam-Rassias

stability of approximately additive mapppings J Math

Anal Appl 184 431-436

Hyers D H (1941) On the stability of the linear functional

equation Proc Nat Acad Sci USA 27 222-224

KimS O, Senthil Kumar B V and Bodaghi A (2017) Stability and

non-stability of the reciprocal-cubic and reciprocal-quartic

functional equations in non-Archimedean fields Adv

Difference Equ 77 1-12

Rassias J M (1982) On approximation of approximately linear

mappings by linear mappings J Funct Anal 46 126-130

Rassias J M, Ravi K and Senthil Kumar B V (2017) A fixed point

approach to Ulam-Hyers stability of duodecic functional

equation in quasi-ß-normed spaces Tbilisi Math J 10 83-

101

Rassias T M (1978) On the stability of the linear mapping in

Banach spaces Proc Amer Math Soc 72 297-300

Ravi K, Rassias J M and Senthil Kumar B V (2010a) Ulam

stability of generalized reciprocal functional equation in

several variables Int J App Math Stat 19 1-19

Ravi K, Rassias J M and Senthil Kumar B V (2010b) Solution

and stability of 2-variable reciprocal functional equation

Bulletin Math Anal Appl 2 84-92

Ravi K, Rassias JM and Senthil Kumar B V (2010c) A fixed point

approach to the generalized Hyers-Ulam stability of

reciprocal difference and adjoint functional equations Thai

J Math 8 469-481

Ravi K, Rassias J M and Senthil Kumar B V (2011) Ulam stability

of reciprocal difference and adjoint functional equations

Aust J Math Anal Appl 8 1-18

Ravi K, Rassias J M and Senthil Kumar B V (2015) Ulam stability

of a generalized reciprocal type functional equation in nonArchimedean fields Arab J Math 4 117-126

Ravi K and Senthil Kumar B V (2010) Ulam-Gavruta-Rassias

stability of Rassias reciprocal functional equation Global

J Appl Math and Math Sci 3 57-79

Ravi K and Senthil Kumar B V (2012) Stability and geometrical

interpretation of reciprocal functional equation Asian J

Current Engg Math 1 300-304

Ravi K and Suresh S (2017) Solution and generalized HyersUlam stability of a reciprocal quadratic functional equation

Int J Pure Appl Math 119 Art. No. AP2017-31-4927

Senthil Kumar B V and Bodaghi A (2017) Estimation of inexact

reciprocal-quintic and reciprocal-sextic functional equations

Mathematica 59 3-14

Senthil Kumar B V and Bodaghi A (2020) Approximation of

Jensen type reciprocal functional equation using fixed point

technique Boletim da Sociedade Paranaense de Matematica

38 125-132

Senthil Kumar B V, Ravi K and Rassias J M (2016a) Solution and

generalized Ulam-Hyers stability of a reciprocal type

functional equation in non-Archimedean fields World

Scientific News 31 71-81

Senthil Kumar B V and Ravi K (2016) Ulam stability of a reciprocal

functional equation in quasi-beta-normed spaces Global J

Pure Appl Math 12 125-128

Senthil Kumar B V, Rassias J M and Ravi K (2016b) Ulam stability

of a bi-reciprocal functional equation in quasi--normed

spaces Novi Sad J Math 46 1-11

Ulam S M (1964) Problems in Modern Mathematics, Chapter

VI, Wiley-Interscience, New York.

Banach spaces J Math Soc Japan 2 64-66

Bodaghi A and Ebrahimdoost Y (2016) On the stability of

quadratic reciprocal functional equation in nonArchimedean fields Asian-Euro J Math 9 1-9

Gavruta P (1994) A generalization of the Hyers-Ulam-Rassias

stability of approximately additive mapppings J Math

Anal Appl 184 431-436

Hyers D H (1941) On the stability of the linear functional

equation Proc Nat Acad Sci USA 27 222-224

KimS O, Senthil Kumar B V and Bodaghi A (2017) Stability and

non-stability of the reciprocal-cubic and reciprocal-quartic

functional equations in non-Archimedean fields Adv

Difference Equ 77 1-12

Rassias J M (1982) On approximation of approximately linear

mappings by linear mappings J Funct Anal 46 126-130

Rassias J M, Ravi K and Senthil Kumar B V (2017) A fixed point

approach to Ulam-Hyers stability of duodecic functional

equation in quasi-ß-normed spaces Tbilisi Math J 10 83-

101

Rassias T M (1978) On the stability of the linear mapping in

Banach spaces Proc Amer Math Soc 72 297-300

Ravi K, Rassias J M and Senthil Kumar B V (2010a) Ulam

stability of generalized reciprocal functional equation in

several variables Int J App Math Stat 19 1-19

Ravi K, Rassias J M and Senthil Kumar B V (2010b) Solution

and stability of 2-variable reciprocal functional equation

Bulletin Math Anal Appl 2 84-92

Ravi K, Rassias JM and Senthil Kumar B V (2010c) A fixed point

approach to the generalized Hyers-Ulam stability of

reciprocal difference and adjoint functional equations Thai

J Math 8 469-481

Ravi K, Rassias J M and Senthil Kumar B V (2011) Ulam stability

of reciprocal difference and adjoint functional equations

Aust J Math Anal Appl 8 1-18

Ravi K, Rassias J M and Senthil Kumar B V (2015) Ulam stability

of a generalized reciprocal type functional equation in nonArchimedean fields Arab J Math 4 117-126

Ravi K and Senthil Kumar B V (2010) Ulam-Gavruta-Rassias

stability of Rassias reciprocal functional equation Global

J Appl Math and Math Sci 3 57-79

Ravi K and Senthil Kumar B V (2012) Stability and geometrical

interpretation of reciprocal functional equation Asian J

Current Engg Math 1 300-304

Ravi K and Suresh S (2017) Solution and generalized HyersUlam stability of a reciprocal quadratic functional equation

Int J Pure Appl Math 119 Art. No. AP2017-31-4927

Senthil Kumar B V and Bodaghi A (2017) Estimation of inexact

reciprocal-quintic and reciprocal-sextic functional equations

Mathematica 59 3-14

Senthil Kumar B V and Bodaghi A (2020) Approximation of

Jensen type reciprocal functional equation using fixed point

technique Boletim da Sociedade Paranaense de Matematica

38 125-132

Senthil Kumar B V, Ravi K and Rassias J M (2016a) Solution and

generalized Ulam-Hyers stability of a reciprocal type

functional equation in non-Archimedean fields World

Scientific News 31 71-81

Senthil Kumar B V and Ravi K (2016) Ulam stability of a reciprocal

functional equation in quasi-beta-normed spaces Global J

Pure Appl Math 12 125-128

Senthil Kumar B V, Rassias J M and Ravi K (2016b) Ulam stability

of a bi-reciprocal functional equation in quasi--normed

spaces Novi Sad J Math 46 1-11

Ulam S M (1964) Problems in Modern Mathematics, Chapter

VI, Wiley-Interscience, New York.

Published

2019-10-04

Section

Research Papers

Copyright (c) 2019 Hemen Dutta, B.V. Senthil Kumar

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