Meir-Keeler type fixed point theorems and dynamics of functions

• Autorzy: Pant R. P.
• Języki publikacji: EN

Abstrakty

EN

In the present paper we obtain a common fixed point theorem under a new contractive condition which is independent of the known contractive definitions. In the second fixed point theorem we study the dynamics of a class of functions induced by real numbers and then apply the result to obtain general tests for divisibility of numbers.

Słowa kluczowe

EN

fixed point theorems; commuting mappings; functions

PL

twierdzenie o punkcie stałym; funkcje

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 1
• Strony: 199--206
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Pant R. P.

• Department of Mathematics, Statistics and Computer Science, G. B. Pant University of Agriculture and Technology, Pantnagar 263145, Uttaranchal, India

Bibliografia

• [1] S. Bernard and J. M. Child, Higher Algebra, Macmillan India Limited, 1994, Delhi.
• [2] J. Jachymski, Common fixed point theorems for some families of maps, Indian J. Pure Appl. Math. 25 (1994), 925-937.
• [3] J. Jachymski, Equivalent conditions and Meir-Keeler type theorems, J. Math. Anal. Appl. 194 (1995), 293-303.
• [4] G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), 771-779.
• [5] G. Jungck, K. B. Moon, S. Park and B. E. Rhoades, On generalization of the Meir-Keeler type contraction maps: Corrections, J. Math. Anal. Appl. 180 (1993), 221-222.
• [6] H. S. Hall and R. S. Knight, Higher Algebra, Macmillan India Limited, 1987, Madras.
• [7] R.A. Holmgren, A First Course in Discrete Dynamical Systems, Springer Verlag, New York, 1994.
• [8] M. Maiti and T. K. Pal, Generalization of two fixed point theorems, Bull. Calcutta Math. Soc. 70 (1978), 57-61.
• [9] R. P. Pant, Common fixed points of weakly commuting mappings, Indian J. Pure. Appl. Math. 17 (1986), 187-192.
• [10] R. P. Pant, Common fixed points of weakly commuting mappings, Math. Student 62 (1993), 97-102.
• [11] R. P. Pant, A contraction principle for four mappings, J. Indian Math. Soc. 66 (to appear).
• [12] R. P. Pant, Discontinuity at fixed points, Ganita 51 (2000), 134-142.
• [13] R. P. Pant, P. C. Joshi and V. Gupta, A Meir-Keeler type fixed point theorem, Indian J. Pure. Appl. Math. 32 (2001), 779-787.
• [14] S. Park and J. S. Bae, Extension of a fixed point theorem of Meir-Keeler, Ark. Math. 19 (1981), 223-228.
• [15] S. Park and B. E. Rhoades, Meir-Keeler type contractive conditions, Math. Japonica 26 (1981), 13-20.
• [16] B. M. Stewart, Theory of Numbers, Macmillan, 1964, New York.