A Family of Hybrid Mappings and Their Fixed Point in Convex Spaces Under Diametral δ Distances

Authors

  • Ladlay Khan

DOI:

https://doi.org/10.5644/SJM.20.02.10

Keywords:

Metrically convex metric space, Occasionally coincidentally commuting mappings, Compatible mappings, Pointwise R-weakly commuting mappings

Abstract

We prove some results on coincidence and common fixed points for compatible as well as pointwise $R$-weakly commuting mappings satisfying a generalized contraction condition on a complete metrically convex metric space that generalize relevant results due to Ciri\'c and Ume \cite{CirićUme}, Khan \cite{Khan13, Khan14}, Rhoades \cite{Rhoades19} and others.

 

Downloads

Download data is not yet available.

References

[1] N. A. Assad, Fixed point theorems for set-valued transformations on compact sets, Boll. Un Mat. Ital., (4) 1973.

[2] N. A. Assad and W. A. Kirk, Fixed point theorems for set valued mappings of contractive type, Pacific J. Math., 43(3) 1972.

[3] Lj. B. CiriĆ and J. S. Ume, Multi-valued non-self mappings on convex metric spaces, Nonlinear Analysis, (60) 2005.

[4] B. Fisher, Common fixed point and contraction mappings satisfying a rational inequality, Math. Sem. Notes, (6) 1978.

[5] O. Hadžić, On coincidence points in convex metric spaces, Univ. U. Novom Sadu, Zb. Rad. Prirod. Mat. Fak. Ser. Mat., 19(2) 1986.

[6] O. Hadžić and Lj. Gajić, Coincidence points for set-valued mappings in convex metric spaces, Univ. U. Novom Sadu, Zb. Rad. Prirod. Mat. Fak. Ser. Mat., 16(1) 1986.

[7] N. J. Huang and Y. J. Cho, Common fixed point theorems for a sequence of set-valued mappings, Korean J. Math. Sci., (4) 1997.

[8] M. Imdad and L. Khan, Rhoades type fixed point theorems for two hybrid pairs of mappings in metrically convex spaces, Nonlinear Analysis Hybrid Systems, (4) 2010.

[9] M. Imdad and L. Khan, Fixed point theorems for a family of hybrid pairs of mappings in metrically convex spaces, Fixed Point Theory Appl., (3) 2005.

[10] S. Itoh, Multi-valued generalized contractions and fixed point theorems, Comment. Math. Univ. Carolinae, (18) 1977.

[11] H. Kaneko and S. Sessa, Fixed point theorems for compatible multi-valued and single-valued mappings, Internat. J. Math. Math. Sci., 12(2) 1989.

[12] K. Kuratowski, Topology, Academic Press, (1) 1966.

[13] L. Khan, Hybrid pairs of nonself multi-valued mappings in metrically convex metric spaces, Global Journal of Pure and Applied Mathematics, 14(11) 2018.

[14] L. Khan, Hybrid pairs of nonself multi-valued mappings in metrically convex spaces, Southeast Asian Bulletin of Mathematics, (46) 2022.

[15] L. Khan and M. Imdad, Rhoades type fixed point theorems for two hybrid pairs of mappings in metrically convex spaces, Applied Math. Computation, (218) 2012.

[16] K. Menger, Untersuchungen tiber allgemeine, Math. Annalen, (100) 1928.

[17] S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30(2) 1969.

[18] R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl., (188) 1994.

[19] B. E. Rhoades, A fixed point theorem for a multivalued nonself mapping, Comment. Math. Univ. Carolinae, 37(2) 1996.

Downloads

Published

10.03.2025

How to Cite

Khan, L. (2025). A Family of Hybrid Mappings and Their Fixed Point in Convex Spaces Under Diametral δ Distances. Sarajevo Journal of Mathematics, 20(2), 281–289. https://doi.org/10.5644/SJM.20.02.10

Issue

Section

Articles