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