Research Article
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Year 2017, , 51 - 59, 30.10.2017
https://doi.org/10.36753/mathenot.421736

Abstract

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 .

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

Year 2017, , 51 - 59, 30.10.2017
https://doi.org/10.36753/mathenot.421736

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.

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 .
There are 13 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Anita Tomar

Shivangi Upadhyay This is me

Ritu Sharma This is me

Publication Date October 30, 2017
Submission Date January 21, 2017
Published in Issue Year 2017

Cite

APA Tomar, A., Upadhyay, S., & Sharma, R. (2017). Strict Coincidence and Common Strict Fixed Point of Hybrid Pairs of Self-mappings with Application. Mathematical Sciences and Applications E-Notes, 5(2), 51-59. https://doi.org/10.36753/mathenot.421736
AMA Tomar A, Upadhyay S, Sharma R. Strict Coincidence and Common Strict Fixed Point of Hybrid Pairs of Self-mappings with Application. Math. Sci. Appl. E-Notes. October 2017;5(2):51-59. doi:10.36753/mathenot.421736
Chicago Tomar, Anita, Shivangi Upadhyay, and Ritu Sharma. “Strict Coincidence and Common Strict Fixed Point of Hybrid Pairs of Self-Mappings With Application”. Mathematical Sciences and Applications E-Notes 5, no. 2 (October 2017): 51-59. https://doi.org/10.36753/mathenot.421736.
EndNote Tomar A, Upadhyay S, Sharma R (October 1, 2017) Strict Coincidence and Common Strict Fixed Point of Hybrid Pairs of Self-mappings with Application. Mathematical Sciences and Applications E-Notes 5 2 51–59.
IEEE A. Tomar, S. Upadhyay, and R. Sharma, “Strict Coincidence and Common Strict Fixed Point of Hybrid Pairs of Self-mappings with Application”, Math. Sci. Appl. E-Notes, vol. 5, no. 2, pp. 51–59, 2017, doi: 10.36753/mathenot.421736.
ISNAD Tomar, Anita et al. “Strict Coincidence and Common Strict Fixed Point of Hybrid Pairs of Self-Mappings With Application”. Mathematical Sciences and Applications E-Notes 5/2 (October 2017), 51-59. https://doi.org/10.36753/mathenot.421736.
JAMA Tomar A, Upadhyay S, Sharma R. Strict Coincidence and Common Strict Fixed Point of Hybrid Pairs of Self-mappings with Application. Math. Sci. Appl. E-Notes. 2017;5:51–59.
MLA Tomar, Anita et al. “Strict Coincidence and Common Strict Fixed Point of Hybrid Pairs of Self-Mappings With Application”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 2, 2017, pp. 51-59, doi:10.36753/mathenot.421736.
Vancouver Tomar A, Upadhyay S, Sharma R. Strict Coincidence and Common Strict Fixed Point of Hybrid Pairs of Self-mappings with Application. Math. Sci. Appl. E-Notes. 2017;5(2):51-9.

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