Strict Coincidence and Common Strict Fixed Point of Hybrid Pairs of Self-mappings with Application

Year 2017, , 51 - 59, 30.10.2017

Anita Tomar , Shivangi Upadhyay Ritu Sharma

https://doi.org/10.36753/mathenot.421736

Cited By: 1

Abstract

In this paper, we discuss strict coincidence and common strict fixed point of strongly tangential hybrid
pairs of self-mappings satisfying Kannan type contraction via δ− distance, which is not even a metric.
Also coincidence and common fixed point is established using Hausdorff metric. Consequently, several
known results are extended, generalized and improved. Examples are given to illustrate our results and
an application is also furnished to demonstrate the applicability of results obtained.

Keywords

Strict common fixed point, strict coincidence point, strongly tangential, hybrid pair

References

• [1] Banach S., Sur les operations dans les ensembles abstrait set leur application aux equations integrals, Fund. Math., 3(1922), 133-181.
• [2] Bellman, R., Methods of Nonlinear Analysis, Vol II, Academic Press, New York, 1973.
• [3] Bellman, R., Lee E. S., Functional equations in dynamic programming, Aequationes Math., 17(1) (1978), 1-18.
• [4] Chauhan, S., Imdad M. , Karapinar E. and B. Fisher, An integral type fixed point theorem for multi-valued mappings employing strongly tangential property, J. Egyptian Math. Soc., 22 (2) (2014), 258-264.
• [5] Imdad, M., Ahmad,A., Kumar, S. On nonlinear nonself hybrid contractions, Radovi Matematicki. 10(2) (2001), 233-244.
• [6] Kaneko, H., A common fixed point of weakly commuting multivalued mappings, Math. Japon., 33(5) (1988), 741-744.
• [7] Kannan, R., Some results on fixed points, Bull. Calcutta Math. Soc., 60(1968), 71-76.
• [8] Kannan, R., Some results on fixed points. II, American Mathematical Monthly, 76, (1969), 405-408.
• [9] Markin, J., A fixed point theorem for set-valued mappings, Bull. Amer. Math. Soc. 74 (1968), 639-640.
• [10] Nadler, Jr. S. B., Multl-valued contraction mappings, Pacific J. Math. 30(1969), 475-486.
• [11] Seesa, S., On a weak commutativity condition of mappings in Fixed point considerations, Publ. Inst. Math. 32 (46), (1982),149-153.
• [12] Sintunavarat, W., Kumam, P., Gregus-type common fixed point theorems for tangential multi-valued mappings of integral type in metric spaces, Int. J. Math. Math. Sci. 12 (2011) . Article ID 923458.
• [13] Subrahmanyam, V., Completeness and fixed-points, Monatsh. Math. 80, (1975), 325-330 .