Research Article
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Year 2017, Volume: 5 Issue: 1, 1 - 12, 01.01.2017

Dipankar Das Nilakshi Goswami Vandana Vandana

https://izlik.org/JA35RE37SF

Abstract

References

  • M.Ackgoz, A review on 2-normed structures, Int. Journal of Math. Analysis, 1(2007), no.4, 187 - 191. MR2340939 (2008e:46012) Zbl 1132.46304.
  • F. F. Bonsal and J. Duncan, Complete Normed algebras, Springer-Verlag, Berlin Heidelberg New York, 1973.
  • Y.J.Cho, M.S.Khan and S.L.Sing, Common fixed points of weakly commuting mappings, Univ.u. Novom Sadu, Zb.Rad. Period.-Mat.Fak.Ser.Mat, 181(1988)129-142. MR1034710
  • D. Das, N. Goswami, Fixed Points of Different Contractive Type Mappings on Tensor Product Spaces, IJIRSET, Vol.3, July 2014, No.7.
  • D. Das, N. Goswami, Fixed Points of Mapping Satisfying a Weakly Contractive Type Condition, Journal of Math. Res. with Appl., Vol 36(2016), No. 1 pp. 70-78.
  • Deepmala and H. K. Pathak, A study on some problems on existence of solutions for nonlinear functional-integral equations, Acta Mathematica Scientia, 33 B(5) (2013), 1305-1313.
  • Deepmala, A Study on Fixed Point Theorems for Nonlinear Contractions and its Applications, Ph.D. Thesis (2014), Pt. Ravishankar Shukla University, Raipur 492 010, Chhatisgarh, India.
  • Deepmala, L.N. Mishra, Differential operators over modules and rings as a path to the generalized differential geometry, FACTA UNIVERSITATIS (NI Š) Ser. Math. Inform. Vol. 30, No. 5 (2015), pp. 753-764.
  • S. Elumalai, R.Vijayaragavan, Characterizations of best approximations in linear 2-normed spaces, General Mathematics Vol. 17, No. 3 (2009), 141-160.
  • S. Gähler, Lineare 2-normierte Riume, Math. Nachr. 28 (1965), 1-43.
  • K. Iseki, Fixed point theorems in 2-metric space, Math.Seminar.Notes, Kobe Univ.,3(1975), 133 - 136. MR0405395.
  • M.S. Khan and M.D. Khan, Involutions with Fixed Points in 2-Banach Spaces, Internat. J. Math. and Math. Sci. VOL. 16 NO. 3 (1993) 429-434.
  • S. S. Kim and Y.J. Cho, Strict Convexity in linear n-normed spaces, Demonstratio Math. 29(1996), no. 4, 739-744.
  • İ. Kisi, S. Büyükkütük, Deepmala, G. Ozturk, AW(k)-type Curves According to Parallel Transport Frame in Euclidean Space E^4, FACTA UNIVERSITATIS (NIÅ ) Ser. Math. Inform. Vol. 31, No. 4 (2016).
  • Z. Liu, X. Zhang, J. Sheok Ume and S. Min Kang, Common fixed point theorems for four mappings satisfying ψ-weakly contractive conditions, Fixed Point Theory and Applications (2015), 1-22 .
  • R. Malčeski, Strong n-convex n-normed spaces, Mat. Bilten 21(1997), 81-102 MR 99m:46059.
  • A. Misiak, n-inner product spaces, Math. Nachr. 140 (1989), 299-319. MR 91a:46021.
  • L.N. Mishra, S.K. Tiwari, V.N. Mishra; Fixed point theorems for generalized weakly S-contractive mappings in partial metric spaces, Journal of Applied Analysis and Computation, Volume 5, Number 4, 2015, pp. 600-612. doi:10.11948/2015047
  • L.N. Mishra, On existence and behavior of solutions to some nonlinear integral equations with Applications, Ph.D. Thesis (2016), National Institute of Technology, Silchar 788 010, Assam, India.
  • L.N. Mishra, M. Sen, R.N. Mohapatra, On existence theorems for some generalized nonlinear functional-integral equations with applications, Filomat, accepted on March 21, 2016, in press.
  • L. N. Mishra, R. P. Agarwal, M. Sen, Solvability and asymptotic behavior for some nonlinear quadratic integral equation involving Erd e lyi-Kober fractional integrals on the unbounded interval, Progress in Fractional Differentiation and Applications Vol. 2, No. 3 (2016), 153-168.
  • L.N. Mishra, H.M. Srivastava, M. Sen, On existence results for some nonlinear functional-integral equations in Banach algebra with applications, Int. J. Anal. Appl., Vol. 11, No. 1, (2016), 1-10.
  • L.N. Mishra, M. Sen, On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order, Applied Mathematics and Computation Vol. 285, (2016), 174-183. DOI: 10.1016/j.amc.2016.03.002
  • L.N. Mishra, S.K. Tiwari, V.N. Mishra, I.A. Khan; Unique Fixed Point Theorems for Generalized Contractive Mappings in Partial Metric Spaces, Journal of Function Spaces, Volume 2015 (2015), Article ID 960827, 8 pages.
  • H.K. Pathak and Deepmala, Common fixed point theorems for PD-operator pairs under Relaxed conditions with applications, Journal of Computational and Applied Mathematics, 239 (2013), 103-113.
  • A. Raymond Ryan, Introduction to Tensor Product of Banach Spaces, London,Springer -Verlag,2002.
  • B.E. Rhoades, Contractive type mappings on a 2-metric space, Math.Nachr.,91(1979), 151 - 155. MR0563606.
  • M. Saha, D. Dey, A. Ganguly and L. Debnath, Fixed Point Theorems for a Class of Weakly C-Contractive Mappings in a Setting of 2-Banach Space, Journal of Mathematics, Volume 2013, Article ID 434205, 7 pages.
  • A. White, 2-Banach spaces, Math.Nachr., 42(1969), 43 - 60. MR0257716 (41 2365) Zbl 0185.20003.

Some fixed point theorems in 2-Banach spaces and 2-normed tensor product spaces

Year 2017, Volume: 5 Issue: 1, 1 - 12, 01.01.2017

Dipankar Das Nilakshi Goswami Vandana Vandana

https://izlik.org/JA35RE37SF

Abstract


Keywords

2-Banach space fixed points

References

  • M.Ackgoz, A review on 2-normed structures, Int. Journal of Math. Analysis, 1(2007), no.4, 187 - 191. MR2340939 (2008e:46012) Zbl 1132.46304.
  • F. F. Bonsal and J. Duncan, Complete Normed algebras, Springer-Verlag, Berlin Heidelberg New York, 1973.
  • Y.J.Cho, M.S.Khan and S.L.Sing, Common fixed points of weakly commuting mappings, Univ.u. Novom Sadu, Zb.Rad. Period.-Mat.Fak.Ser.Mat, 181(1988)129-142. MR1034710
  • D. Das, N. Goswami, Fixed Points of Different Contractive Type Mappings on Tensor Product Spaces, IJIRSET, Vol.3, July 2014, No.7.
  • D. Das, N. Goswami, Fixed Points of Mapping Satisfying a Weakly Contractive Type Condition, Journal of Math. Res. with Appl., Vol 36(2016), No. 1 pp. 70-78.
  • Deepmala and H. K. Pathak, A study on some problems on existence of solutions for nonlinear functional-integral equations, Acta Mathematica Scientia, 33 B(5) (2013), 1305-1313.
  • Deepmala, A Study on Fixed Point Theorems for Nonlinear Contractions and its Applications, Ph.D. Thesis (2014), Pt. Ravishankar Shukla University, Raipur 492 010, Chhatisgarh, India.
  • Deepmala, L.N. Mishra, Differential operators over modules and rings as a path to the generalized differential geometry, FACTA UNIVERSITATIS (NI Š) Ser. Math. Inform. Vol. 30, No. 5 (2015), pp. 753-764.
  • S. Elumalai, R.Vijayaragavan, Characterizations of best approximations in linear 2-normed spaces, General Mathematics Vol. 17, No. 3 (2009), 141-160.
  • S. Gähler, Lineare 2-normierte Riume, Math. Nachr. 28 (1965), 1-43.
  • K. Iseki, Fixed point theorems in 2-metric space, Math.Seminar.Notes, Kobe Univ.,3(1975), 133 - 136. MR0405395.
  • M.S. Khan and M.D. Khan, Involutions with Fixed Points in 2-Banach Spaces, Internat. J. Math. and Math. Sci. VOL. 16 NO. 3 (1993) 429-434.
  • S. S. Kim and Y.J. Cho, Strict Convexity in linear n-normed spaces, Demonstratio Math. 29(1996), no. 4, 739-744.
  • İ. Kisi, S. Büyükkütük, Deepmala, G. Ozturk, AW(k)-type Curves According to Parallel Transport Frame in Euclidean Space E^4, FACTA UNIVERSITATIS (NIÅ ) Ser. Math. Inform. Vol. 31, No. 4 (2016).
  • Z. Liu, X. Zhang, J. Sheok Ume and S. Min Kang, Common fixed point theorems for four mappings satisfying ψ-weakly contractive conditions, Fixed Point Theory and Applications (2015), 1-22 .
  • R. Malčeski, Strong n-convex n-normed spaces, Mat. Bilten 21(1997), 81-102 MR 99m:46059.
  • A. Misiak, n-inner product spaces, Math. Nachr. 140 (1989), 299-319. MR 91a:46021.
  • L.N. Mishra, S.K. Tiwari, V.N. Mishra; Fixed point theorems for generalized weakly S-contractive mappings in partial metric spaces, Journal of Applied Analysis and Computation, Volume 5, Number 4, 2015, pp. 600-612. doi:10.11948/2015047
  • L.N. Mishra, On existence and behavior of solutions to some nonlinear integral equations with Applications, Ph.D. Thesis (2016), National Institute of Technology, Silchar 788 010, Assam, India.
  • L.N. Mishra, M. Sen, R.N. Mohapatra, On existence theorems for some generalized nonlinear functional-integral equations with applications, Filomat, accepted on March 21, 2016, in press.
  • L. N. Mishra, R. P. Agarwal, M. Sen, Solvability and asymptotic behavior for some nonlinear quadratic integral equation involving Erd e lyi-Kober fractional integrals on the unbounded interval, Progress in Fractional Differentiation and Applications Vol. 2, No. 3 (2016), 153-168.
  • L.N. Mishra, H.M. Srivastava, M. Sen, On existence results for some nonlinear functional-integral equations in Banach algebra with applications, Int. J. Anal. Appl., Vol. 11, No. 1, (2016), 1-10.
  • L.N. Mishra, M. Sen, On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order, Applied Mathematics and Computation Vol. 285, (2016), 174-183. DOI: 10.1016/j.amc.2016.03.002
  • L.N. Mishra, S.K. Tiwari, V.N. Mishra, I.A. Khan; Unique Fixed Point Theorems for Generalized Contractive Mappings in Partial Metric Spaces, Journal of Function Spaces, Volume 2015 (2015), Article ID 960827, 8 pages.
  • H.K. Pathak and Deepmala, Common fixed point theorems for PD-operator pairs under Relaxed conditions with applications, Journal of Computational and Applied Mathematics, 239 (2013), 103-113.
  • A. Raymond Ryan, Introduction to Tensor Product of Banach Spaces, London,Springer -Verlag,2002.
  • B.E. Rhoades, Contractive type mappings on a 2-metric space, Math.Nachr.,91(1979), 151 - 155. MR0563606.
  • M. Saha, D. Dey, A. Ganguly and L. Debnath, Fixed Point Theorems for a Class of Weakly C-Contractive Mappings in a Setting of 2-Banach Space, Journal of Mathematics, Volume 2013, Article ID 434205, 7 pages.
  • A. White, 2-Banach spaces, Math.Nachr., 42(1969), 43 - 60. MR0257716 (41 2365) Zbl 0185.20003.
There are 29 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Dipankar Das This is me

Nilakshi Goswami This is me

Vandana Vandana This is me

Publication Date January 1, 2017
IZ https://izlik.org/JA35RE37SF
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Das, D., Goswami, N., & Vandana, V. (2017). Some fixed point theorems in 2-Banach spaces and 2-normed tensor product spaces. New Trends in Mathematical Sciences, 5(1), 1-12. https://izlik.org/JA35RE37SF
AMA 1.Das D, Goswami N, Vandana V. Some fixed point theorems in 2-Banach spaces and 2-normed tensor product spaces. New Trends in Mathematical Sciences. 2017;5(1):1-12. https://izlik.org/JA35RE37SF
Chicago Das, Dipankar, Nilakshi Goswami, and Vandana Vandana. 2017. “Some Fixed Point Theorems in 2-Banach Spaces and 2-Normed Tensor Product Spaces”. New Trends in Mathematical Sciences 5 (1): 1-12. https://izlik.org/JA35RE37SF.
EndNote Das D, Goswami N, Vandana V (January 1, 2017) Some fixed point theorems in 2-Banach spaces and 2-normed tensor product spaces. New Trends in Mathematical Sciences 5 1 1–12.
IEEE [1]D. Das, N. Goswami, and V. Vandana, “Some fixed point theorems in 2-Banach spaces and 2-normed tensor product spaces”, New Trends in Mathematical Sciences, vol. 5, no. 1, pp. 1–12, Jan. 2017, [Online]. Available: https://izlik.org/JA35RE37SF
ISNAD Das, Dipankar - Goswami, Nilakshi - Vandana, Vandana. “Some Fixed Point Theorems in 2-Banach Spaces and 2-Normed Tensor Product Spaces”. New Trends in Mathematical Sciences 5/1 (January 1, 2017): 1-12. https://izlik.org/JA35RE37SF.
JAMA 1.Das D, Goswami N, Vandana V. Some fixed point theorems in 2-Banach spaces and 2-normed tensor product spaces. New Trends in Mathematical Sciences. 2017;5:1–12.
MLA Das, Dipankar, et al. “Some Fixed Point Theorems in 2-Banach Spaces and 2-Normed Tensor Product Spaces”. New Trends in Mathematical Sciences, vol. 5, no. 1, Jan. 2017, pp. 1-12, https://izlik.org/JA35RE37SF.
Vancouver 1.Das D, Goswami N, Vandana V. Some fixed point theorems in 2-Banach spaces and 2-normed tensor product spaces. New Trends in Mathematical Sciences [Internet]. 2017 Jan. 1;5(1):1-12. Available from: https://izlik.org/JA35RE37SF