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SET-VALUED PREŠIĆ-CHATTERJEA TYPE CONTRACTIONS AND FIXED POINT THEOREMS

Year 2016, Volume: 29 Issue: 2, 473 - 478, 21.06.2016

Abstract

In this paper, we establish some common fixed point theorems for two mappings satisfying set-valued Pre\v{s}i\'{c}-Chatterjea type contractive conditions. The new theorems generalize and unify some well-known theorems of the literature. We also provide some examples to illustrate and confirm the usability of the obtained results.

References

  • M. S. Khan, M. Berzig, and B. Samet, Some convergence results for iterative
  • sequences of Preˇsi´c type and applications, Advances in Difference Equations
  • (2012). doi:10.1186/1687-1847-2012-38
  • N. Shahzad, S. Shukla, Set-valued G-Preˇsi´c operators on metric spaces endowed
  • with a graph and fixed point theorems, Fixed Point Theory Appl., (In Press).
  • R. Kannan, Some results on fixed point, Bull. Calcutta Math. Soc., 60, 71-
  • (1968).
  • S. Reich, Some remarks concerning contraction mappings, Canad. Nth. Bull., 14,
  • -124(1971) MR 45# 1145
  • S. Shukla, Some stability results and Assad-Kirk type fixed point theorems for setvalued
  • Preˇsi´c type mappings, Journal of Nonlinear and Convex Analysis, (in
  • press)
  • S. Shukla, R. Sen, S. Radenovi´c, Set-valued Preˇsi´c type contraction in metric
  • spaces, An. S¸ tiint¸. Univ. Al. I. Cuza Ias¸i. Mat. (N.S.) (in press)
  • S. Shukla, R. Sen, Set-valued Preˇsi´c-Reich type mappings in metric spaces, Revista
  • de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A.
  • Matematicas (2012). DOI 10.1007/s13398-012-0114-2
  • S. Shukla, Set-valued Preˇsic´-C´ iric´ type contraction in 0-complete partial metric
  • spaces, Matemati´cki Vesnik, 66(2), 178-189 (2014)
  • S. Shukla, S. Radenovi´c, Some generalizations of Preˇsi´c type mappings and applications,
  • An. S¸ tiint¸. Univ. Al. I. Cuza Ias¸i. Mat. (N.S.) (accepted)(2014).
  • S.B. Nadler Jr., Multi-valued contraction mappings, Pac. J. Math. 30, 475-488
  • (1969)
  • S.B. Preˇsi´c, Sur la convergence des suites, Comptes. Rendus. de l’Acad. de Paris,
  • , 3828-3830 (1965)
  • S.B. Preˇsi´c, Sur une classe dinequations aux differences finite et sur la convergence
  • de certaines suites, Publ. de lInst. Math. Belgrade, 5(19), 75-78 (1965)
  • S.K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci., 25, 727-730
  • (1972)
  • Y. Z. Chen, A Preˇsi´c type contractive condition and its applications, Nonlinear
  • Anal., doi:10.1016/j.na.2009.03.006 (2009)

Set-Valued Prešić-Chatterjea Type Contractions and Fixed

Year 2016, Volume: 29 Issue: 2, 473 - 478, 21.06.2016

Abstract

References

  • M. S. Khan, M. Berzig, and B. Samet, Some convergence results for iterative
  • sequences of Preˇsi´c type and applications, Advances in Difference Equations
  • (2012). doi:10.1186/1687-1847-2012-38
  • N. Shahzad, S. Shukla, Set-valued G-Preˇsi´c operators on metric spaces endowed
  • with a graph and fixed point theorems, Fixed Point Theory Appl., (In Press).
  • R. Kannan, Some results on fixed point, Bull. Calcutta Math. Soc., 60, 71-
  • (1968).
  • S. Reich, Some remarks concerning contraction mappings, Canad. Nth. Bull., 14,
  • -124(1971) MR 45# 1145
  • S. Shukla, Some stability results and Assad-Kirk type fixed point theorems for setvalued
  • Preˇsi´c type mappings, Journal of Nonlinear and Convex Analysis, (in
  • press)
  • S. Shukla, R. Sen, S. Radenovi´c, Set-valued Preˇsi´c type contraction in metric
  • spaces, An. S¸ tiint¸. Univ. Al. I. Cuza Ias¸i. Mat. (N.S.) (in press)
  • S. Shukla, R. Sen, Set-valued Preˇsi´c-Reich type mappings in metric spaces, Revista
  • de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A.
  • Matematicas (2012). DOI 10.1007/s13398-012-0114-2
  • S. Shukla, Set-valued Preˇsic´-C´ iric´ type contraction in 0-complete partial metric
  • spaces, Matemati´cki Vesnik, 66(2), 178-189 (2014)
  • S. Shukla, S. Radenovi´c, Some generalizations of Preˇsi´c type mappings and applications,
  • An. S¸ tiint¸. Univ. Al. I. Cuza Ias¸i. Mat. (N.S.) (accepted)(2014).
  • S.B. Nadler Jr., Multi-valued contraction mappings, Pac. J. Math. 30, 475-488
  • (1969)
  • S.B. Preˇsi´c, Sur la convergence des suites, Comptes. Rendus. de l’Acad. de Paris,
  • , 3828-3830 (1965)
  • S.B. Preˇsi´c, Sur une classe dinequations aux differences finite et sur la convergence
  • de certaines suites, Publ. de lInst. Math. Belgrade, 5(19), 75-78 (1965)
  • S.K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci., 25, 727-730
  • (1972)
  • Y. Z. Chen, A Preˇsi´c type contractive condition and its applications, Nonlinear
  • Anal., doi:10.1016/j.na.2009.03.006 (2009)
There are 31 citations in total.

Details

Journal Section Mathematics
Authors

Satish Shukla

Publication Date June 21, 2016
Published in Issue Year 2016 Volume: 29 Issue: 2

Cite

APA Shukla, S. (2016). SET-VALUED PREŠIĆ-CHATTERJEA TYPE CONTRACTIONS AND FIXED POINT THEOREMS. Gazi University Journal of Science, 29(2), 473-478.
AMA Shukla S. SET-VALUED PREŠIĆ-CHATTERJEA TYPE CONTRACTIONS AND FIXED POINT THEOREMS. Gazi University Journal of Science. June 2016;29(2):473-478.
Chicago Shukla, Satish. “SET-VALUED PREŠIĆ-CHATTERJEA TYPE CONTRACTIONS AND FIXED POINT THEOREMS”. Gazi University Journal of Science 29, no. 2 (June 2016): 473-78.
EndNote Shukla S (June 1, 2016) SET-VALUED PREŠIĆ-CHATTERJEA TYPE CONTRACTIONS AND FIXED POINT THEOREMS. Gazi University Journal of Science 29 2 473–478.
IEEE S. Shukla, “SET-VALUED PREŠIĆ-CHATTERJEA TYPE CONTRACTIONS AND FIXED POINT THEOREMS”, Gazi University Journal of Science, vol. 29, no. 2, pp. 473–478, 2016.
ISNAD Shukla, Satish. “SET-VALUED PREŠIĆ-CHATTERJEA TYPE CONTRACTIONS AND FIXED POINT THEOREMS”. Gazi University Journal of Science 29/2 (June 2016), 473-478.
JAMA Shukla S. SET-VALUED PREŠIĆ-CHATTERJEA TYPE CONTRACTIONS AND FIXED POINT THEOREMS. Gazi University Journal of Science. 2016;29:473–478.
MLA Shukla, Satish. “SET-VALUED PREŠIĆ-CHATTERJEA TYPE CONTRACTIONS AND FIXED POINT THEOREMS”. Gazi University Journal of Science, vol. 29, no. 2, 2016, pp. 473-8.
Vancouver Shukla S. SET-VALUED PREŠIĆ-CHATTERJEA TYPE CONTRACTIONS AND FIXED POINT THEOREMS. Gazi University Journal of Science. 2016;29(2):473-8.