On Generalized Contraction Principles over S-metric Spaces with Application to Homotopy

Debashis Dey; Kushal Roy; Mantu Saha

EN

On Generalized Contraction Principles over S-metric Spaces with Application to Homotopy

Abstract

In the present paper, we introduce the concept of a class of generalized contraction mappings called A-contraction on S-metric space and investigate the existence of fixed points over such spaces. Analogue result has been formulated in integral setting over such an S-metric space. Moreover, the result is applied to homotopy theory. -

Keywords

Fixed point, A-contraction, S-metric space

References

S.Gahler, 2-metric Raume and ihre topologische strucktur, Math. Nachr. 26 (1963) 115-148.
S.Gahler, Lineare 2-normietre Raume, Math. Nachr. 28 (1965) 1-43.
K. S. Ha, Y. J. Cho, and A. White, Strictly convex and strictly 2-convex 2-normed spaces, Mathematica Japonica 33(3) 1988 375-384.
B.C. Dhage, Generalized metric spaces mappings with fixed point, Bull. Calcutta Math. Soc. 84 (1992) 329-336.
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006) 289-297.
S. Sedghi, K.P.R. Rao, N. Shobe, Common fixed point theorems for six weakly compatible mappings in D*-metric spaces, Internat J. Math. Math. Sci. 6 (2007) 225-237.
S. Sedghi, N. Shobe, H. Zhou, A common fixed point theorem in D*-metric spaces, Fixed Point Theory Appl. (2007) Article ID 27906 13 pages.
S. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik 64(3) (2012) 258-266.
S. Sedghi and N. V. Dung, Fixed point theorems on S-metric spaces, Mat. Vesnik 66(1) (2014) 113-124.
M. Akram, A. A. Siddiqui, A fixed point theorem for A-contractions on a class of generalised metric spaces, Korean J. Math. Sciences 10(2) (2003) 1-5.

M. Akram, A. A. Zafar, A. A. Siddiqui, A general class of contractions: A- contractions, Novi Sad J. Math. 38(1) (2008) 25-33.
M. Saha, D. Dey, Fixed point theorems for a class of A-contractions on a 2-metric space, Novi Sad J. Math. 40(1) (2010) 3-8.
A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci 29(9) (2002) 531-536.
D. Dey, A. Ganguly, M. Saha, Fixed point theorems for mappings under general contractive condition of integral type, Bull. Math. Anal. Appl. 3(1) (2011) 27-34.
B.E . Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, International Journal of Mathematics and Mathematical Sciences 63 (2003) 4007- 4013.
C. Vetro, F. Vetro, A Homotopy Fixed Point Theorem in 0-Complete Partial Metric Space, Filomat 29(9) (2015) 2037-2048.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Debashis Dey This is me
India

Kushal Roy ^* This is me
India

Mantu Saha This is me
India

Publication Date

June 30, 2020

Submission Date

January 9, 2019

Acceptance Date

April 9, 2020

Published in Issue

Year 2020 Number: 31

IZ

https://izlik.org/JA25TA99PW

APA

Dey, D., Roy, K., & Saha, M. (2020). On Generalized Contraction Principles over S-metric Spaces with Application to Homotopy. Journal of New Theory, 31, 95-103. https://izlik.org/JA25TA99PW

AMA

1.Dey D, Roy K, Saha M. On Generalized Contraction Principles over S-metric Spaces with Application to Homotopy. JNT. 2020;(31):95-103. https://izlik.org/JA25TA99PW

Chicago

Dey, Debashis, Kushal Roy, and Mantu Saha. 2020. “On Generalized Contraction Principles over S-Metric Spaces With Application to Homotopy”. Journal of New Theory, nos. 31: 95-103. https://izlik.org/JA25TA99PW.

EndNote

Dey D, Roy K, Saha M (June 1, 2020) On Generalized Contraction Principles over S-metric Spaces with Application to Homotopy. Journal of New Theory 31 95–103.

IEEE

[1]D. Dey, K. Roy, and M. Saha, “On Generalized Contraction Principles over S-metric Spaces with Application to Homotopy”, JNT, no. 31, pp. 95–103, June 2020, [Online]. Available: https://izlik.org/JA25TA99PW

ISNAD

Dey, Debashis - Roy, Kushal - Saha, Mantu. “On Generalized Contraction Principles over S-Metric Spaces With Application to Homotopy”. Journal of New Theory. 31 (June 1, 2020): 95-103. https://izlik.org/JA25TA99PW.

JAMA

1.Dey D, Roy K, Saha M. On Generalized Contraction Principles over S-metric Spaces with Application to Homotopy. JNT. 2020;:95–103.

MLA

Dey, Debashis, et al. “On Generalized Contraction Principles over S-Metric Spaces With Application to Homotopy”. Journal of New Theory, no. 31, June 2020, pp. 95-103, https://izlik.org/JA25TA99PW.

Vancouver

1.Debashis Dey, Kushal Roy, Mantu Saha. On Generalized Contraction Principles over S-metric Spaces with Application to Homotopy. JNT [Internet]. 2020 Jun. 1;(31):95-103. Available from: https://izlik.org/JA25TA99PW