Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Some Fixed Point Theorems for Single Valued and Set Valued Maps


Affiliations
1 Department of Mathematics, Central University of Kashmir, Nowgam-Srinagar 190 015, India
2 Department of Mathematical Sciences, Islamic University of Science and Technology, Awantipora Pulwama 192 122, Jammu and Kashmir, India
     

   Subscribe/Renew Journal


In this paper we introduce the concept of single valued map and set valued map and set valued map and obtain new types of contraction mappings both for single valued map and set valued maps and establish new fixed point theorems in this direction.
User
Subscription Login to verify subscription
Notifications
Font Size

  • Amine A. Harandi and D. Oregan, Fixed point theorem for set valued contraction type maps in metric space: Fixed point theory and Application, Vol. 662010, 7 (2010), Article ID 390183.
  • S. Banach, Surles operation dansles essembles abstraits et leur applications aux equations.
  • D. W. Boyd and J. S. W. Wang, On non-linear contractions, Proc. Am. Math Soc., 20 (1969) 458–464.
  • S. K. Chatterjea, Fixed point theorems, CR Acad. Bulgare Sci., 25 (1972) 727–730.
  • L. Ciric, Generalized contractions and fixed point theorems, Pub. Inst. Math. (Belgr), 12(26) (1971) 14–26.
  • L. Ciric, A generalization of Banach contraction principle, Proc. and Math. Soc., 48(12) (1974) 267–273.
  • L. Ciric, Multivalued non-linear contraction mappings, Non-linear Analysis, 71 (1974) 2716–2723.
  • P. Z. Daffer and H. Kaneko, Fixed points of generalized contractive multivalued mappings, J. Math. Anals. Appl., 192 (1995) 655–666.
  • N. Hassain, V. Parvanveh, Bessem Samet and C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces.
  • D. S. Jaggi, Some ubique fixed point theorems, Indian J. Pure Appl. Math., 8(Z) (1977) 223–230.
  • M. Jleli and B. Samet, A new generalization of Banach contraction principle, J. Inequality Appl., 138 (2014).
  • R. Kannan, Some results on fixed points, Bult. Math. Soc., 60 (1968) 71–76.
  • D. Klim and Wardowske, Fixed point theorem for set valued contraction in a complete metric space, J. Math, Anal-Appl., 334(1) (2007).
  • E. Karapinar, P. Kuman and P. Salimi, On α − ψ Meir-keeler contraction mappings, Fixed Point Theory Appl., 194 (2013)
  • A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969) 326–329.
  • N. Mizoguchi and W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric space, J. Math. Anal. and Appl., 141(1) (1989).
  • S. B. Nadler, Multivalued contraction mappings, Pac. J. Math., 30 (1969) 475–488.
  • H. K. Nashine, M. Imadad and M. Hassan, Common fixed point theorems under rational contraction in complete valued metric space, J. Non-linear Sci. Appl., 7 (2014) 42–50.
  • M. Ozturk and M. Basarir, On some common fixed point theorems with rational expressions on some metric spaces, J. Math. Stat., (2) (2012) 211–222.
  • S. Reich, Some remarks concering contraction mappings, Can. Math. Bull., 14 (1971) 121–124.
  • S. Reich, Some fixed point problems, Atti Acad. Naz. Lincei, 57 (1974) 194–198.
  • B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α−ψ contraction type mappings, Non-linear Anal., 75 (2012) 2154–2165.
  • T. Suzuki, Mizagushi-Takahashis fixed point theorem is a real generalization of Nadlers, J. Math. Appl., (2007).
  • K. Tayab, Mizagushi-Takahashis type fixed point theorem, Computer and Math. Appl., 57 (2009) 507–511.
  • D. Wardowski, Fixed points of new type of contraction mappings on complete metric space, Fixed Point Theory Appl., 94 (2012).
  • H. K. Xu, Metric fixed point theory of multivalued mappings, Dissertations Math. (RozprawyMat.), 389(39) (2000).

Abstract Views: 167

PDF Views: 0




  • Some Fixed Point Theorems for Single Valued and Set Valued Maps

Abstract Views: 167  |  PDF Views: 0

Authors

Shabir Ahanger
Department of Mathematics, Central University of Kashmir, Nowgam-Srinagar 190 015, India
Bilal A. Chat
Department of Mathematical Sciences, Islamic University of Science and Technology, Awantipora Pulwama 192 122, Jammu and Kashmir, India

Abstract


In this paper we introduce the concept of single valued map and set valued map and set valued map and obtain new types of contraction mappings both for single valued map and set valued maps and establish new fixed point theorems in this direction.

References