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A common fixed point theorem for T-contractions on generalized cone \lowercase{b}-metric spaces

Pagidi Mallikarjun Reddy|Manhala Rangamma
대한수학회 (The Korean Mathematical Society)|2017.01|대한수학회논문집 (Communications of the KMS)|제32권 제1호|pp. 65-74

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키워드

fixed pointcommon fixed pointcone rectangular metric spacegeneralized cone b-metric space$T$-contraction
주제분류수학

초록

In this paper, we establish a unique common fixed point theorem for $T$-contraction of two self maps on generalized cone b-metric spaces with solid cone. The result of this paper improves and generalizes several well-known results in the literature. Two examples are also given to support the result.

Abstract

In this paper, we establish a unique common fixed point theorem for $T$-contraction of two self maps on generalized cone b-metric spaces with solid cone. The result of this paper improves and generalizes several well-known results in the literature. Two examples are also given to support the result.

참고문헌 (10)

  1. A. Azam, "Banach contraction principle on cone rectangular metric spaces", Appl. Anal. Discrete Math, 3(2), pp.236~241 (2009)
  2. I. A. Bakhtin, "The contraction mapping principle in quasi metric spaces", Functional analysis, (30), pp.26~37 (1989), Ul’yanovsk. Gos. Ped. Inst.
  3. S. Banach, "Surles operations dans les ensembles abstraits et leur application aux equa-tions integrales", Fundamenta Mathematicae, 3, pp.133~181 (1922)
  4. A. Beiranvand, "Two fixed point theorems for special mappings", arxiv:0903.1504v1 math.FA, ~ (2009)
  5. A. Branciari, "A fixed point theorem of Banach-Caccippoli type on a class of generalized metric spaces", Publ. Math. Debrecen, 57(1-2), pp.31~37 (2000)
  6. R. George, "Generalized cone b-metric spaces and contraction principles", Mat. Vesnik, 67(4), pp.246~257 (2015)
  7. R. George, "Rectangular b-metric spaces and contraction principle", J. Nonlinear Sci. Appl, 8, pp.1005~1013 (2015)
  8. L. G. Huang, "Cone metric spaces and fixed point theorems of contractive mappings", J. Math. Anal. Appl, 332(2), pp.1468~1476 (2007)
  9. N. Hussain, "KKM mappings in cone b-metric spaces", Comput. Math. Appl, 62(4), pp.1677~1684 (2011)
  10. G. Jungck, "Common fixed point theorems for weakly compatible pairs on cone metric spaces", Fixed Point Theory Appl, 2009, pp.13~ (2009)

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